October 2026 - Converting Fractions into Decimals Study Guide

The method, and when to skip it

A fraction is a division waiting to happen: 3/8 means 3 divided by 8, which is 0.375. With a calculator provided, this is a keystroke — but you will not always want to reach for it, because a question that asks you to order five values is five divisions if you do not know the common ones.

Going the other way is easier still. Read the last decimal place to get the denominator: 0.45 ends in the hundredths, so it is 45/100, which simplifies to 9/20.

The conversions worth knowing on sight

These cover the overwhelming majority of what appears on the exam.

Building on what you know

You do not need to memorise every fraction — the multiples come free once you know the unit fraction.

• Know 1/8 = 0.125, and 5/8 is five of them: 0.625.
• Know 1/5 = 0.2, and 3/5 is 0.6.
• Anything over 10, 100 or 1000 needs no division at all — just move the point.
• A denominator that divides into 100 is easy: 7/20 is 35/100, so 0.35.

Ordering a mixed set

Terms to know

Terminating decimal

A decimal that ends, such as 0.375.

Repeating decimal

A decimal with a digit or block that repeats forever, such as 0.333….

Place value

What each digit is worth by position: tenths, hundredths, thousandths.

Rounding

Adjusting to a given number of places, looking at the next digit to decide.

Truncating

Cutting a decimal short without rounding. A source of wrong answers, not a method.

What the TEAS asks most

The same core ideas appear in different wording. If you can answer these without stopping to think, you have what this section requires.

Key points

• A fraction is a division: numerator ÷ denominator.
• To go from decimal to fraction, read the last place value as the denominator, then simplify.
• Memorise halves, thirds, quarters, fifths, eighths and tenths.
• Multiples come free: knowing 1/8 gives you 3/8, 5/8 and 7/8.
• Round rather than truncate, and convert a mixed list to one form before comparing.