The Correct Answer and Explanation is:
The correct answer is 156.25.
The mathematical problem shown in the image is 1 ÷ 0.0064. This calculation asks how many times the decimal 0.0064 fits into the number 1. To solve this without a calculator, we can convert the problem into a more manageable form by eliminating the decimal from the divisor.
First, let’s express the division problem as a fraction:
1 / 0.0064
The main challenge here is dividing by a decimal. We can simplify this by converting the denominator, 0.0064, into a whole number. We can do this by multiplying it by a power of 10. Since 0.0064 has four digits after the decimal point, we need to multiply it by 10,000 to make it a whole number. Multiplying 0.0064 by 10,000 moves the decimal point four places to the right, which gives us 64.
To keep the overall value of the fraction the same, we must also multiply the numerator, which is 1, by the same number, 10,000. This is a core rule of fractions: multiplying the numerator and denominator by the same non-zero number results in an equivalent fraction. So, 1 multiplied by 10,000 equals 10,000.
Our new, equivalent problem is now a division of two whole numbers:
10,000 ÷ 64
Now we can perform long division to find the solution.
- We start by dividing 100 by 64. It goes in 1 time, with a remainder of 36 (100 – 64 = 36).
- Next, we bring down the next digit from 10,000, which is a 0, to make our new number 360. We divide 360 by 64. This goes in 5 times (5 × 64 = 320), with a remainder of 40 (360 – 320 = 40).
- We bring down the last 0 from 10,000, making our number 400. We divide 400 by 64. This goes in 6 times (6 × 64 = 384), with a remainder of 16 (400 – 384 = 16).
- Since we have a remainder, we place a decimal point in our answer and add a 0 to the remainder, making it 160. We divide 160 by 64. This goes in 2 times (2 × 64 = 128), with a remainder of 32 (160 – 128 = 32).
- Finally, we add another 0 to our remainder, making it 320. We divide 320 by 64. This goes in exactly 5 times (5 × 64 = 320), with no remainder.
By combining the digits from our long division, we find that 10,000 divided by 64 is 156.25.
