The steps to convert 37 over 4 to a decimal are shown below:
Division is shown with divisor 4, quotient 9.21, and dividend 37 labeled as Step 1. The numbers below 37 in sequence are subtract 36 lebeled as Step 2, 10 labeled as Step 3, subtract 6 labeled as step 4, 4, subtract 4, and 0.
In what step is the first error?
Answers
Answer:
Step 4
Step-by-step explanation:
We are given that
[tex]\frac{37}{4}[/tex]
We have to convert [tex]\frac{37}{4}[/tex] into decimal.
Divisor:The number which divides the dividend.
Dividend:The number which is divided by divisor.
Quotient:The number obtained when the divisor divides the dividend.
[tex]\frac{37}{4}=9.25[/tex]
Step:1
Dividend 37
Step 2:
37
-36
=1
Step 3:
10
Step 4:
10
-8
=2
Step 5:
20
-20
=0
Hence, the first error in step 4.
Related Questions
I need help with this question about similar triangles
Answers
Answer:
ST = 12 units
Step-by-step explanation:
Δ RAS and Δ TES are similar triangles, thus the ratios of corresponding sides are equal, that is, noting that SR = 21 - ST, thus
[tex]\frac{ST}{SR}[/tex] = [tex]\frac{TE}{AR}[/tex] substitute values
[tex]\frac{ST}{21-ST}[/tex] = [tex]\frac{8}{6}[/tex] ( cross- multiply )
6ST = 8(21 - ST)
6ST = 168 - 8ST ( add 8ST to both sides )
14ST = 168 ( divide both sides by 14 )
ST = 12
Abigail has a cylindrical candle mold with the dimensions shown. If Abigail has a rectangular block of wax measuring 15 cm by 12 cm by 18 cm, about how many candles can she make after melting the block of wax? Round to the nearest tenth.
Answers
Find the volume of the candle using the formula for volume of a cylinder:
V = PI x r^2 x h = 3.14 x 3.4^2 x 6 = 217.79 cubic cm. Round to 217.8
Find the volume of the block: V = l x w x h = 15 x 12 x 18 = 3,240 cubic cm.
Now divide the volume of the block by the volume of a candle:
3240 / 217.8 = 14.88
Round to the nearest tenth = 14.9 candles.
Number of cylindrical candles after melting the rectangular block is 14.9.
What is cylinder?" Cylinder is a three dimensional surface formed by two parallel lines and two parallel circular base."
What is volume?" Volume is the total amount of space occupied by any 3 dimensional body."
Formula used
Volume of a cylinder = π r²h
Volume of a rectangular block = length × width ×height
According to the question,
Height of a cylinder = 6cm
radius of cylinder = 3.4cm
Length of a block = 15cm
width of a block = 12cm
height of a block = 18cm
Volume of a cylinder = [tex]3.14[/tex]× [tex](3.4)^{2}[/tex]×[tex]6[/tex]
=217.8 cubic cm
Volume of rectangular block = [tex]15[/tex] × [tex]12[/tex] × [tex]18[/tex]
= 3240 cubic cm
Number of candles = Volume of rectangular block / volume of cylinder
= [tex]\frac{3240}{217.8}[/tex]
= 14.88
= 14.9 (nearest tenth)
Hence the Number of cylindrical candles after melting the rectangular block is 14.9.
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The stopping distance of a car is modeled by the function d = 0.05r(r + 2) where d is the stopping distance of the car measured in feet and r is the speed of the car in miles per hour. If skid marks left on the road are 75 feet long, how fast was the car traveling?
Answers
Answer:
The car was moving approximately at a speed of 37.74 miles per hour.
Step-by-step explanation:
We are given the following in the question:
The stopping distance of a car is given by
[tex]d = 0.05r(r + 2)[/tex]
where d is the stopping distance in feet and r is speed of the car in miles per hour.
The stopping distance is 75 feet, we have to find the speed of the car,
Putting d = 75 in the equation, we get,
[tex]75 = 0.05r(r + 2)\\r^2 + 2r = 1500\\r^2 + 2r-1500 = 0\\\\r =\dfrac{-2\pm \sqrt{4-(4)(1)(-1500)}}{2}\\\\r\approx -39.74,37.74[/tex]
Thus, the car was moving approximately at a speed of 37.74 miles per hour.
Step 1: 5 = negative 2 (negative StartFraction 3 Over 10 EndFraction) + b. Step 2: 5 = StartFraction 6 Over 10 EndFraction + b. Step 3: 5 minus StartFraction 6 Over 10 EndFraction = StartFraction 6 Over 10 EndFraction minus StartFraction 6 Over 10 EndFraction + b. Step 4: StartFraction 50 Over 10 EndFraction minus StartFraction 6 Over 10 EndFraction = b. Step 5: StartFraction 44 Over 10 EndFraction = b. Step 6: y = negative 2 x minus 4.4.
A student used the slope-intercept form to write the equation of a line that has a slope of -2 and passes through the point (StartFraction negative 3 Over 10 EndFraction, 5). The student’s work is shown to the left.
Analyze the steps to identify the error.
Step1: student switched the x and y values
Step 3: student needed to add StartFraction 6 Over 10 EndFraction to both sides
Step 5: student subtracted incorrectly
Step 6: student needed to add the b value
Answers
Answer:
D.) Step 6: student needed to add the b value.
Step-by-step explanation:
I got it wrong and it gave me the right answer, which is what i provided, D.
Answer: Step6
Step-by-step explanation:
In the United States, 13 out of 20 cans are recycled. What percent of cans are recycled?
Answers
Answer:
65%
Step-by-step explanation:
Divide 13 by 20:
0.65
Times 100:
65
So 65%
5. Alisha's average math test score was 82. Which of the following students has the same average
math test score as Alisha?
F. Jenny earned 492 points on 6 tests.
G. Frankie earned 352 points on 4 tests.
H. Benicio earned 468 points on 6 tests.
1. Dontonio earned 344 points on 4 tests.
(20 Points)
Answers
Answer:
F. Jenny earned 492 points on 6 tests.
Jenny has the same average
math test score as Alisha i.e. 82.
Step-by-step explanation:
Points earned by Jenny = 492
no. of maths tests attempted by Jenny = 6
average maths test score = 492/6
=82
Why a quadratic function f whose zeros are 2 and 7
Answers
A quadratic function whose zeros are 2 and 7 is [tex]f(x) = x^2 - 9x+14[/tex]
If the zeros of a quadratic function are a and b, the quadratic function will be given as:
f(x) = (x - a)(x - b)
For the function f(x) whose zeros are 2 and 7:
f(x) = (x - 2)(x - 7)
Expand the equation
[tex]f(x)=x^2-7x-2x+14\\\\f(x) = x^2 - 9x+14[/tex]
Therefore, a quadratic function whose zeros are 2 and 7 is [tex]f(x) = x^2 - 9x+14[/tex]
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Final answer:
A quadratic function with zeros at 2 and 7 can be constructed by multiplying (x - 2) and (x - 7), leading to the function f(x) = (x - 2)(x - 7). A constant 'a' scales the function, which, if not specified, can be assumed to be 1 for simplicity.
Explanation:
The question asks about constructing a quadratic function f with zeros at 2 and 7. In mathematics, a quadratic function is of the form f(x) = ax2 + bx + c, where a, b, and c are constants and a ≠ 0.
To construct a quadratic function with zeros 2 and 7, we utilize the fact that if 2 and 7 are zeros, the function must be divisible by (x - 2) and (x - 7).
Hence, f(x) can be written as f(x) = a(x - 2)(x - 7), where a is a non-zero constant that scales the function.
To determine a, more information about the function is needed, such as a specific value f(x) takes at a certain point.
In the absence of additional information, we can assume a = 1 for simplicity, which gives us the specific quadratic function f(x) = (x - 2)(x - 7).
This function will cross the x-axis at x = 2 and x = 7, making them its zeros.
What is the value of n in the equation 1 (n – 4) – 3 = 3 - (2n+3)?
Answers
Answer:
n=7/3
Step-by-step explanation:
1 (n – 4) – 3 = 3 - (2n+3)
1. distribute the 1 on the left side and distribute the -1 on the right side
1n-4-3=3-2n-3
2. add like terms
1n-7=-2n
3. move n to one side and by itself
-7=-3n
4. divide -3 to get n alone. Both negatives cancel out each other
7/3=n
Step-by-step explanation:
[tex]1(n-4)-3=3-(2n+3)[/tex]
[tex]n-4-3=3-2n-3\\n+2n=3-3+3+4\\3n=7\\n=\frac{7}{3}[/tex]
Proof
[tex]1(n-4)-3=3-(2n+3)[/tex]
[tex]1(\frac{7}{3} -4)-3=3-[2(\frac{7}{3}) +3]\\1(\frac{7-12}{3} )-3=3-(\frac{14}{3} +3)\\1(\frac{-5}{3} )-3=3-(\frac{14+9}{3})\\\frac{-5}{3} -3=3-(\frac{23}{3})[/tex]
[tex]\frac{-5-9}{3} =\frac{9-23}{3} \\\frac{-14}{3} =\frac{-14}{3}[/tex]
Complete the steps to derive the standard form of the equation of a
circle centered at Alh, k).
1. What is segment AB to circle A?
Check
Answers
Answer:
a radius
x-h
y-k
x-h, y-k
Step-by-step explanation:
The standard form of the circle is given by ( x - h )² + ( y - k )² = r²
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the equation of circle be C
Let the center of the circle be represented as A ( h , k )
Now , the radius of the circle is = r units
And , standard form of a circle is
( x - h )² + ( y - k )² = r²
when it is a unit circle , the center is at ( 0 , 0 )
S0 , the equation of circle is x² + y² = r²
Hence , the standard form of circle is ( x - h )² + ( y - k )² = r²
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GEOMETRY! Show your work, please.
Answers
Answer:
90°
Step-by-step explanation:
By inscribed angle theorem:
[tex]m\angle STU = \frac{1}{2} \times 180 \degree = 90 \degree[/tex]
Last fall, a middle school took a group of students on a trip to Space Camp, which is 360 miles away. The bus that they took to Space Camp traveled at a constant speed, and it took them 6 hours to get from the school to the camp. How many miles did the bus travel in 1 hour?
Answers
Answer:
The bus travelled 60 miles in 1 hour.
Step-by-step explanation:
To solve this problem we need to calculate the average speed at which the bus travelled. This is given by the distance travelled divided by the time that they took to get there. So we have:
average speed = distance/time
average speed = 360/6
average speed = 60 miles/h
Therefore in 1 hour they travelled 60 miles.
A toy soldier set a selection of 6 weapons for 3 soldiers.
How many different ways can the 3 soldiers be assigned weapons if each soldier is to be assigned only one weapon?
Answers
Answer:
2
Step-by-step explanation:
There are 120 different ways to assign 6 weapons to 3 soldiers, each receiving one weapon, calculated using permutations.
Calculating Permutations for Weapons Assignment
To determine how many different ways 3 soldiers can be assigned weapons from a selection of 6, we need to calculate the permutations of 6 objects taken 3 at a time. We use the permutation formula, which is expressed as P(n, k) = n! / (n-k)!, where n is the total number of items, and k is the number of items to choose. In this case, n is 6 (the total number of weapons), and k is 3 (the total number of soldiers).
We calculate the permutations as follows:
6! / (6-3)! = (6 * 5 * 4) / (3 * 2 * 1) = 120 ways.
Therefore, there are 120 different ways to assign the weapons to the soldiers, with each soldier getting one weapon.
The point (−7, -24) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
Answers
Answer:
[tex]\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960[/tex]
[tex]\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280[/tex]
[tex]\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429[/tex]
Step-by-step explanation:
The point is in the 3rd Quadrant of the Cartesian Plane. Therefore, angle must be between 180° and 270° with respect to the horizontal.
The angle is:
[tex]\theta = 180^{\textdegree}+\tan^{-1}\left(\frac{24}{7} \right)[/tex]
[tex]\theta \approx 253.740^{\textdegree}[/tex]
The values of the trigonometrical functions are computed below:
[tex]\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960[/tex]
[tex]\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280[/tex]
[tex]\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429[/tex]
A dealer sold a car to a man and made
a propit of 15%. The man then sold it
to a woman for 120,175 at a loss of 5%. How much did the dealer buy the car
Answers
Answer:
110.000
Step-by-step explanation:
Selling at a loss of 5% means it was sold for 95% of its purchase value.
If 120.175 equals to 95% then 100%(the purchase value) is 126.500.
120.175/95*100 = 126.500 (plenty of other ways to calculate this, but this is one of the easiest)
So now we change to the dealer's perspective, he sold the car for 126.500 and for him that meant a 15% profit. If the purchase value is 100%, then the sale value is 115% (purchase value+15% profit)
Calculate the purchase value:
126.500/115*100 = 110.000
The dealer bought the car for 110.000, sold it for 126.500, so he made a profit of 16.500 (126.500-110.000) which is a 15% profit (15% of 110.000 is 16.500).
Please help me answer this
Answers
Answer:
B. 3
Step-by-step explanation:
If you flip a coin 300 times how many times would you expect the coin to lands head up ? Explain your reasoning (write in complete, mathematically precise sentences).
Answers
Answer: you would expect it to flip about 150 times heads.
Step-by-step explanation: A coin has two sides. There's an equal chance for each side. So 50-50 chance.
300 divided by 2 is 150
(Sorry if it's not the best mathematical way to say it)
A right triangle has a side with length 20 meters, hypotenuse with length 25 meters, and side labeled b. StartRoot 5 EndRoot m 5 m StartRoot 45 EndRoot m 15 m
Answers
Answer:
15 m
Step-by-step explanation:
25² = 20² + b²
625 = 400 + b²
b² = 225
b = 15
it is 15 hope this helped and good luck...
Students set a goal of collecting 900 cans for the canned food drive. The number of cans they have collected so far is 82% of their goal. How many cans have they collected so far?
Answers
Answer:
738 cans.
Step-by-step explanation:
To calculate 82% of 900, take 0.82 *900. Your answer will be 738.
Answer:
738 cans
Step-by-step explanation:
900 x .82=738
can anybody help please?
Answers
Answer:
AB = 24 cm, BC = 6 cm
Step-by-step explanation:
The perimeter of PQRS = 2(8) + 2(2) = 16 + 4 = 20 cm
Given the perimeter of ABCD is 60 cm, then
scale factor = [tex]\frac{60}{20}[/tex] = 3
That is the dimensions of ABCD are 3 times those of PQRS, so
AB = 3 × 8 cm = 24 cm
BC = 3 × 2 cm = 6 cm
Answer:
AB = 24 cm.
BC = 6 cm.
Step-by-step explanation:
The outer rectangle is a dilation of the inner rectangle centered at the origin. Therefore:
The inner and outer rectangles are similar so the ratio of length to width of the outer rectangle is the same as the ratio of length to width of the inner one.
so AB / BC = 8/2 = 4
AB = 4BC -------------(1)
Also as the perimeter = 60
2AB + 2BC = 60.............(2)
Substituting AB = 4BC in equation (2):
2(4BC) + 2BC = 60
10BC = 60
BC = 6 cm.
and AB = 4*6 = 24 cm.
Anyone can help me with all of these answers 1-10 ( 18 Points ) ?
Answers
Answer:
1) 14
2) 8
3) 5
4) 11
5) 10
6) 6
7) 10
8) 17
9) 26
10) 18
Step-by-step explanation:
Merry Early Christmas :)
what’s the coordinate grid ?
Answers
Answer:
linear and lateral
Step-by-step explanation:
thsts it
Final answer:
A coordinate grid, also known as a Cartesian coordinate system, is a mechanism used in mathematics to define every point in a plane with a pair of numerical values indicating horizontal and vertical positions from an origin. Systems like UTM and SPC are derived from this concept, using a grid to simplify plotting and calculations on a plane surface.
Explanation:
A coordinate grid, or a Cartesian coordinate system, is a tool used in mathematics to specify each point uniquely in a plane by a pair of numerical coordinates. These are typically written as an ordered pair (x, y) where 'x' represents the horizontal displacement and 'y' represents the vertical displacement, both measured from a specific origin point. This system of geometry was developed by René Descartes, hence the name Cartesian.
For example, the origin of a coordinate system is the starting point where both x and y are zero, designated as (0,0). If we move to the right, x increases, and if we move up, y increases. Conversely, moving to the left decreases x and moving down decreases y. So, for instance, the point (3,4) is located 3 units to the right of the origin and 4 units above it.
Plane coordinate systems, like the Universal Transverse Mercator (UTM) and the State Plane Coordinate (SPC) systems, simplify calculations by using a grid pattern superimposed on a flattened representation of the Earth's surface, facilitating easier and more precise location plotting than spherical coordinate systems like latitude and longitude.
If a toy helicopter is moving at 12 m/s, how much energy does 3kg toy have?
Answers
9514 1404 393
Answer:
216 J
Step-by-step explanation:
The kinetic energy is given by ...
KE = 1/2mv^2
KE = (1/2)(3 kg)(12 m/s)^2 = 216 kg·m²/s² = 216 J
The kinetic energy of the toy is 216 joules.
__
Its potential energy depends on its height.
Answer:216 J Is the answer I just checked
Step-by-step explanation:
Identify the equation that represents the line of best fit on this scatter plot.
Answers
Answery
y= 2x+2
Step-by-step explanation:
The temperature inside a freezer was –18 °C when the freezer was accidentally unplugged. After that, the temperature increased by 2 °C per hour. This situation can be modeled by an equation of the form y = mx + b , where x = the time in hours that the freezer was been unplugged and y = the temperature in degrees Celsius. What is the value of b in this equation?
Answers
Answer:
-18
Step-by-step explanation:
b is where the line crosses the y-axis, or where x=0. Since it starts at -18, then that would be the b.
a loaded truck is traveling 20 mph faster than a freight train. In the time it takes the train to travel 160 miles, the truck travels 240 miles. find the speed of the truck
Answers
To find the speed of the truck, start by assigning the speed of the train as 'x', then the truck's speed is 'x + 20'. Set up an equation based on the principle of time = distance/speed, make them equal to each other then solve for 'x'. The truck's speed will be 'x + 20'.
Explanation:Let's call the speed of the freight train 'x' (in mph). We know from the question, that the loaded truck is traveling 20 mph faster than the train, so the truck's speed is 'x + 20' mph.
Given that the time it takes for the train to travel 160 miles is the same time it takes the truck to travel 240 miles, we can write an equation based on the principle that time equals distance divided by speed.
For the train, time = 160/x and for the truck, time = 240/(x+20). As both times are equal, we can write the equation as:
160/x = 240/(x + 20).
Solving this equation for 'x' will give us the speed of the freight train in mph. Then, by adding 20 to 'x', we can find the speed of the truck.
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in the adjoining figure P A and PB are tangents from P to a circle with Centre O if angle APB is equal to 40 degree then find angle ACB
Answers
Step-by-step explanation:
40° + 90° + 90° + angle ACB = 360°
220° + angle ACB = 360°
angle ACB = 360° - 220°
Therefore angle ACB = 140°
Hope it will help :)
Final answer:
To find angle ACB, determine angle AOB by subtracting the tangents' right angles and angle APB from 360 degrees, which results in 140 degrees. Then, using the Inscribed Angle Theorem, angle ACB is half the measure of angle AOB, yielding 70 degrees.
Explanation:
The student is asking how to find the angle ACB when given that PA and PB are tangents to a circle with centre O, and angle APB is 40 degrees. To find angle ACB, which is the angle at the circle subtended by the chord AB, we first determine the measure of angle AOB, which is central and subtended by AB as well. Since the tangents from a point outside a circle form a right angle with the radius at the point of contact, we have two right triangles OAP and OBP, each with an angle of 90 degrees. These right angles add to the given angle APB to form a full angle around point P which is 360 degrees. Knowing angle APB is 40 degrees, we can find angle AOB by subtracting the sum of the two right angles and angle APB from 360 degrees.
Angle AOB = 360 degrees - (90 degrees + 90 degrees + 40 degrees) = 360 degrees - 220 degrees = 140 degrees
Finally, since angle ACB is inscribed and angle AOB is central, both subtended by the same chord AB, angle ACB is half the measure of angle AOB by the Inscribed Angle Theorem. Therefore, angle ACB is 70 degrees.
Angle ACB = ½ * Angle AOB = ½ * 140 degrees = 70 degrees
A motorboat takes 5 hours to travel 200 miles going upstream. The return trip takes 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Answers
Answer:
rate of motorboat: b
rate of current: c
So the rate the boat travels upstream is $b - c$, and the rate it travels downstream is $b + c$
Step-by-step explanation:
d = rt
200 = (b - c)\cdot 5
200 = (b + c)\cdot 4
b - c = 40
b + c = 50
Adding these equations, we get:
2b = 90
b = 45
So
c = 50 - 45 = 5
Therefore the rate of the boat is 45kph, and the rate of the current is 5kph
Hope this helps :)
Final answer:
The boat has a speed of 45 mph in still water, and the current runs at 5 mph. By using the given times and distances for upstream and downstream travel, we can set up equations to solve for the boat's speed and the current's speed.
Explanation:
To find the rate of the boat in still water and the rate of the current, let's denote the boat's speed in still water as b and the speed of the current as c. When the boat goes upstream, its effective speed is b - c, and when it goes downstream, its effective speed is b + c. We can translate this into two equations based on the information given:
(b - c) × 5 hours = 200 miles (upstream)
(b + c) × 4 hours = 200 miles (downstream)
By dividing the distance by the time, we can solve for the effective speeds upstream and downstream.
b - c = 200 miles / 5 hours = 40 mph
b + c = 200 miles / 4 hours = 50 mph
Add these two equations:
2b = 90 mph
b = 45 mph (boat's speed in still water)
Next, subtract the first equation from the second:
2c = 10 mph
c = 5 mph (current's speed)
So, the boat has a speed of 45 mph in still water, and the current has a speed of 5 mph.
IF I DOG WALK AND FOR EACH DOG I MAKE $15 HOW MANEY DOGS DO I HAVE TO WALK TO GET $100
Answers
Answer:
7
Step-by-step explanation:
A triangle has one angle that measures 35º. Which values could be the measures of the other two angles?
Answers
Answer:
See below.
Step-by-step explanation:
The 3 angles in a triangle add up to 180 degrees, so the sum of the other 2 angles is 180 - 35 = 145 degrees.
So, for example the other 2 angles could be 60 and 85 degrees.
Answer:
75° and 70°
25° and 120°
90° and 55°
Step-by-step explanation:
I got it right
how do i covert a fraction into a decimal.
Answers
Answer:
By dividing the top number by the bottom.
Step-by-step explanation:
ummmmm
To convert a fraction into a decimal, divide the fraction's numerator by its denominator. Multiplying a decimal by 100 converts it to a percent, and dividing a percent by 100 converts it back into a decimal. This process is used to manipulate numerical values for various mathematical applications.
Explanation:Converting a Fraction to a Decimal
To convert a fraction into a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number). For example, to convert 3/4 to a decimal, you divide 3 by 4, which equals 0.75. If the fraction is not in simplest form, you may first simplify it before dividing. This is a basic mathematical skill that you will use in many areas of math.
To convert a decimal to a percent, you multiply the decimal by 100. For instance, 0.75 multiplied by 100 equals 75%, because you are essentially finding how many 'parts out of 100' are present in the decimal.
In the case of converting percents, to turn a percent into a decimal, you divide by 100. So, taking 75% and dividing by 100 would give you 0.75, which is the original decimal we started with.
Another example is converting 0.0479 into a decimal that's a number between 1 and 10. To do this, we would move the decimal point to the right two places to get 4.79, as specified by the conversion factor which helps in adjusting units or scaling numbers without changing the value.