What is 40 7/200 as a decimal?

Decimals and fractions are two ways you can write the same number. A decimal is written when in two parts, its whole numbers part and its decimals part – with a decimal point in between. In this article, you’ll learn how to convert 40 7/200 to a decimal using the division method.

Solution: 40 7/200 as a decimal is 40.03

Methods

First step – Making the fraction improper:

The first step to changing 40 7/200 into a decimal is to change it to an improper fraction. To do that, we need to multiply 40 by 200 and add its product to 7 in the numerator to get: 8007/200. Now we will attempt to convert 8007/200 to a decimal using one of the following methods:

Method 1 – Explanation using the division method:

A fraction is usually split into two parts: the first part is the number on top, called the numerator; and the second part is the number on the bottom, called the denominator. These are both separated by a line called the “divisor line”. We can use the division method help to solve this question: to get a decimal, simply divide the numerator 8007 by the denominator 200 (which you can enter in any calculator):

8007 (numerator) ÷ 200 (denominator) = 40.03

And finally, you get 40.03 as your answer when you convert 40 7/200 (or 8007/200) to a decimal.

Method 2 – Explanation using the factors of 10 method:

Sometimes, dividing a number by a power of 10 (like 10, 100, 1000 etc.) is easy because all you need to do is move the invisible decimal place left by how many zeros you have in the power of 10. But for this question, the denominator, 200, isn’t a power of 10.

However, we can change the fraction: if the denominator is a factor of a power of 10, like 2, 4, 5, 8, 10, 16, 20, 25, 40, 50 and so on, then we can convert the fraction into one that is easy to calculate.

To do this, we need to make the denominator to a power of 10 - to make 200 a power of 10, we need to multiply by 5 (200 * 5 = 1000). We multiplied the denominator by 5, so now we need to also multiply the numerator by 5 too:

$\frac{8007 * 5}{200 * 5} = \frac{40035}{1000} = 40.03$

And finally, you get 40.03 as your answer when you convert 40 7/200 (or 8007/200) to a decimal. 8 Math Hacks and Tricks to Turn Your ‘Okay’ Math Student Into a Math Champion!

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