Relationship between percentages, fractions, and decimals

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)

NA4-5

New NZC (2026)

NZC26-P4-NUM-FIN-K-Y9-01
NZC26-P4-NUM-NSO-K-Y9-03
NZC26-P4-NUM-FIN-K-Y9-02
NZC26-P4-NUM-NSO-P-Y9-16
NZC26-P4-NUM-NSO-P-Y9-14
NZC26-P4-NUM-NSO-P-Y9-01
NZC26-P4-NUM-NSO-P-Y9-04
NZC26-P4-NUM-NSO-K-Y9-06
NZC26-P4-NUM-NSO-P-Y9-18
NZC26-P4-NUM-FIN-P-Y9-01
NZC26-P3-NUM-NSO-K-Y7-17
NZC26-P3-NUM-NSO-K-Y7-21
NZC26-P3-NUM-NSO-K-Y8-08
NZC26-P3-NUM-NSO-P-Y7-18
NZC26-P3-NUM-NSO-P-Y7-19

Resources

Alpha textbook: Intro to percentage, Ex 9.01, pg 143
Alpha textbook: Converting between PFD, Ex 9.02-9.04, pg 144-145
CorbettMaths worksheetQuestions PDF · Answers
Beta: Skills in Ex 3.13, pg 62

Terminology

Percentage
Fraction
Decimal
Convert
Numerator
Denominator
Equivalent
Recurring decimal

Task goals

Read a shaded area model (hundred grid, fraction bar, or fraction circle) and state the shaded amount as a fraction in simplest form, a decimal, and a percentage.
Convert a fraction to a decimal and a percentage, and a decimal or percentage back to a fraction in simplest form.
Convert between a decimal and a percentage by multiplying or dividing by 100, including values above 100% and recurring decimals.
Compare and order values given in mixed forms (fractions, decimals, percentages) by converting each to a common form.
Convert a recurring decimal to a fraction in simplest form using the algebraic method (e.g. multiplying by a power of 10 and subtracting).
Apply fraction-decimal-percentage equivalence to real-world comparison problems (test scores, shares, discounts, mixtures).

Where this fits

What leads into this objective, and where it goes next.

Before

Place Values and Decimals

Standard Form (Scientific Notation)

Powers & Roots

You are here

$Relationship between percentages, fractions, and decimals$

Relationship between percentages, fractions, and decimals

Know

Percentages are a way of expressing a fraction of 100.

Statement▸

Year 9 · Number · Financial mathematics

NZC26-P4-NUM-FIN-K-Y9-01

Know

There are an infinite number of rational numbers between any two numbers; these can be represented by terminating decimals, recurring decimals, and fractions.

Statement▸

Year 9 · Number · Number structures and operations

NZC26-P4-NUM-NSO-K-Y9-03