What is 1 67/10 as a decimal?

Solution: 1 67/10 as a decimal is 7.7

Methods

First step – Making the fraction improper:

The first step to changing 1 67/10 into a decimal is to change it to an improper fraction. To do that, we need to multiply 1 by 10 and add its product to 67 in the numerator to get: 77/10. Now we will attempt to convert 77/10 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 77 by the denominator 10 (which you can enter in any calculator):

77 (numerator) ÷ 10 (denominator) = 7.7

And finally, you get 7.7 as your answer when you convert 1 67/10 (or 77/10) 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, 10, 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 10 a power of 10, we need to multiply by 1 (10 * 1 = 10). We multiplied the denominator by 1, so now we need to also multiply the numerator by 1 too:

\frac{77 * 1}{10 * 1} = \frac{77}{10} = 7.7

And finally, you get 7.7 as your answer when you convert 1 67/10 (or 77/10) to a decimal.

Practice more conversion problems

All it takes to be better at something is some practice! Take a look at some more similar problems on converting fractions to decimals and give them a go:

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