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Basic 5 · Mathematics · Counting, Representation and Cardinality

Comparing and Ordering Numbers up to 1,000,000

In this topic you will compare and order numbers up to 1,000,000 using the symbols >, < and =.

By the end of these notes you should be able to:

  • Compare two numbers using place value
  • Use the symbols >, < and = correctly
  • Arrange numbers in ascending and descending order

What you already know

  • Reading and writing numbers up to 1,000,000

Copy everything that has a blue line on its left into your notebook. The other parts are for reading.

Strand
Number
Sub-strand
Counting, Representation and Cardinality
Indicator
B5.1.1.1.4-5 – Compare and order whole numbers up to 1,000,000 and represent the comparison using >, < or =

Introduction

The Ashanti Region and the Greater Accra Region have the largest populations in Ghana. To know which is larger, we compare their numbers digit by digit.

1. Steps for Comparing

  1. Count the digits. The number with more digits is greater.
  2. If they have the same number of digits, compare from the left (the highest place).
  3. The first place where the digits are different decides which number is greater.

Example 1

Compare 584,312 and 548,912.

  1. Both have 6 digits.
  2. Hundred thousands: 5 = 5.
  3. Ten thousands: 8 > 4.

Answer: 584,312 > 548,912

Example 2

Compare 99,999 and 100,000.

  1. 99,999 has 5 digits; 100,000 has 6 digits.

Answer: 99,999 < 100,000

Comparison symbols
SymbolMeaningExample
>greater than700,001 > 699,999
<less than245,300 < 245,310
=equal to500 thousands = 500,000

2. Ordering Numbers

Ascending order: From the smallest to the largest.

Descending order: From the largest to the smallest.

Example 3

Arrange 306,450; 360,045; 305,640; 360,450 in ascending order.

  1. Hundred thousands are all 3.
  2. Ten thousands: 0, 6, 0, 6 → 306,450 and 305,640 are smaller.
  3. Compare 306,450 and 305,640: thousands 6 > 5, so 305,640 is smallest.
  4. Compare 360,045 and 360,450: hundreds 0 < 4.

Answer: 305,640; 306,450; 360,045; 360,450

A number line from 300,000 to 370,000 with four numbers placed in order
Figure 1: Ordering large numbers Place three 6-digit numbers on a number line.Illustration: Sirbus

Tip: Line the numbers up in a column by place value. It is easier to compare.

3. Comparing in Real Life

Comparing large numbers helps people make decisions. A district planner compares the populations of towns to decide where to build new schools and clinics. A trader compares prices to find the best buy. When numbers are written in different forms, change them all to figures first. For example, to compare "six hundred thousand" and 599,999, write the first as 600,000. Both numbers now have six digits. The hundred thousands digits are 6 and 5, so 600,000 > 599,999.

New words

compare
To decide which is greater or smaller.
greater than
Larger than; symbol >.
less than
Smaller than; symbol <.
ascending
From smallest to largest.
descending
From largest to smallest.
digit
One of the symbols 0 to 9.

Summary

  • A number with more digits is greater.
  • With the same number of digits, compare from the left.
  • > means greater than, < means less than, = means equal.
  • Ascending goes up; descending goes down.

Class activity: Population Ranking

  1. Use number cards showing the populations of six towns (from your teacher).
  2. Arrange them in descending order.
  3. Write three comparison statements using > and <.

You need: Place-value chart on manila card, Locally made large-number cards, Exercise books

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. Which symbol makes this true? 450,200 ___ 450,020

    • A. >
    • B. <
    • C. =
    • D. +
    Show answer
    Answer: >2 hundreds > 0 hundreds.

  2. 2. Which number is the smallest?

    • A. 690,999
    • B. 691,000
    • C. 609,999
    • D. 690,000
    Show answer
    Answer: 609,999Its ten thousands digit is 0.

  3. 3. Which list is in descending order?

    • A. 800,000 → 780,000 → 708,000
    • B. 708,000 → 780,000 → 800,000
    • C. 780,000 → 800,000 → 708,000
    • D. 800,000 → 708,000 → 780,000
    Show answer
    Answer: 800,000 → 780,000 → 708,000Largest to smallest.

  4. 4. 1,000,000 > 999,999

    • A. True
    • B. False
    Show answer
    Answer: TrueIt has more digits.

  5. 5. 312,980 > 312,989

    • A. True
    • B. False
    Show answer
    Answer: False980 < 989.

  6. 6. 400 thousands ______ 400,000 (write >, < or =)

    Show answer
    Answer: =They are equal.

  7. 7. Arrange in ascending order: 521,300; 512,300; 521,030.

    Show answer
    Answer: 512,300; 521,030; 521,300Compare place by place.

  8. 8. Write the largest and smallest 6-digit numbers you can make with 4, 0, 9, 2, 7, 1.

    Show answer
    Answer: Largest 974,210; smallest 102,4790 cannot be the first digit of the smallest.

Homework

  1. Find the prices of three expensive items (car, land, house) in an advert. Order them from cheapest to dearest.