NZ Level 4 Convert thousandths between simplified fractions and decimals
Lesson

When we rename fractions as tenths, hundredths or thousandths, we are also able to use our knowledge of place value to then write our fraction as a decimal.

Remember how we converted fractions to decimals, using tenths and hundredths? This time, we'll use a similar approach, but look at thousandths.

## Place value

Place value is important when we express numbers in decimals. Let's say we want to compare $0.353$0.353 and $0.6$0.6. We may think that because $353$353 is larger than $6$6, that $0.353$0.353 is larger than $0.6$0.6, but we can see when we use a place value table, this is not the case.

Place value
Units . Tenths Hundredths Thousandths
0 . 3 5 3
0 . 6 0 0

$0.6$0.6 is actually $6$6 tenths, where $0.353$0.353 only has $3$3 tenths, so is smaller. Similarly, if we consider them both as fractions of a thousand, then $0.6$0.6 is $\frac{600}{1000}$6001000, which is more than $\frac{353}{1000}$3531000.

## Changing our fractions to thousandths

The first thing we need to do is rename our fraction so that it is expressed in thousandths if it's not already in thousandths. This video shows you how to convert your fraction to thousandths, allowing you to then easily change it to decimals. By the way, renaming our fractions to thousandths is not changing the value of our number at all, we're just finding an equivalent fraction.

Remember!

To convert fractions to decimals, you can rename them to tenths, hundredths or thousandths.

#### Examples

##### Question 1

Write the fraction $\frac{11}{200}$11200 as a decimal.

##### QUESTION 2

Write the decimal $0.872$0.872 as a fraction in simplest form.

##### QUESTION 3

Write the number represented by $98$98 thousandths:

1. As a simplified fraction.
2. As a decimal.

### Outcomes

#### NA4-6

Know the relative size and place value structure of positive and negative integers and decimals to three places.