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Everyday English · Place value, number forms, explaining a number and checking a written answer

Math Talk: 18 English Words for Place Value and Number Forms

Read and explain numbers in standard, word, expanded and unit forms; use accurate English for digits, zero placeholders, regrouping and comparisons.

Suggested Grades 3–518 everyday words8 light-review questions
Learning objectiveRead four representations of the same whole number, explain what a zero does, and compare numbers using exact place-value language.

What to do

Maths problems often ask for a number in a particular form. In elementary place-value work, standard form means the ordinary numeral, such as 4,305. In other branches of mathematics, the words 'standard form' can have other meanings, so always read the question's context.

For 4,305, word form is 'four thousand three hundred five'; expanded form is 4,000 + 300 + 5; and one complete unit form is '4 thousands, 3 hundreds, 0 tens, 5 ones.' The zero tens can be omitted when naming only nonzero units, but it cannot be ignored when placing digits in the numeral.

The digit 3 has different values in 3,405 and 4,305. A digit is a symbol; its place value is the amount it represents in that position. In 4,305, 3 means 300 rather than 3.

Read a number aloud, build it in a place-value chart, write it in different forms, and then check by adding the parts. For example, four hundred six is 406, not 4,006; the latter is four thousand six. The examples use whole numbers, not decimal place values.

Core everyday words

place value

noun phrase · PLAYS VAL-yoo

the value a digit has because of its position in a number

Example: The 4 in 4,208 has a value of four thousand.

digit

noun · DIJ-it

one of the ten symbols 0 through 9

Example: The number 502 has three digits.

number

noun · NUM-ber

a mathematical value that can be written in several ways

Example: The number 305 can be written in words.

ones

plural noun · WUNZ

the place that counts single units

Example: In 524, the 4 is in the ones place.

tens

plural noun · TENZ

the place that counts groups of ten

Example: In 524, the 2 is in the tens place.

hundreds

plural noun · HUN-dredz

the place that counts groups of one hundred

Example: In 524, the 5 means five hundreds.

thousands

plural noun · THOW-zundz

the place that counts groups of one thousand

Example: In 5,024, the 5 is in the thousands place.

standard form

noun phrase · STAN-derd FORM

writing a whole number using its usual digits

Example: 4,305 is the standard form of four thousand three hundred five.

word form

noun phrase · WERD FORM

writing a number using number words

Example: Four hundred six is the word form of 406.

expanded form

noun phrase · ik-SPAN-did FORM

writing a number as a sum of its nonzero place values

Example: 4,305 = 4,000 + 300 + 5.

unit form

noun phrase · YOO-nit FORM

naming how many units of each place are present

Example: 4 thousands 3 hundreds 0 tens 5 ones is a unit form of 4,305.

numeral

noun · NOO-mer-ul

a written symbol or group of symbols representing a number

Example: 406 is a numeral for four hundred six.

regroup

verb · ree-GROOP

trade units for an equal value in different place-value units

Example: Regroup 10 ones as 1 ten.

compose

verb · kum-POHZ

put parts together to make a number

Example: Compose 300 + 40 + 2 to make 342.

decompose

verb · dee-kum-POHZ

break a number into parts that add to the same total

Example: Decompose 607 as 600 + 7.

compare

verb · kum-PAIR

decide how two numbers are related in size

Example: Compare 507 and 570 by checking the tens place.

greater than

phrase · GRAY-ter THAN

describing a number that is larger than another

Example: 570 is greater than 507.

less than

phrase · LES THAN

describing a number that is smaller than another

Example: 507 is less than 570.

Recognise the form

Recognise the form

Choose the mathematically equivalent representation.

Multiple choice

1. Which is the standard form of 'four thousand three hundred five'?

  1. 4,305
  2. 4,035
  3. 4,350
  4. 43,005
Multiple choice

2. Which is the expanded form of 607?

  1. 600 + 7
  2. 60 + 7
  3. 600 + 70
  4. 6,000 + 7
Multiple choice

3. Which is a correct unit form of 2,040?

  1. 2 thousands and 4 tens
  2. 2 hundreds and 4 tens
  3. 2 thousands and 4 ones
  4. 2 hundreds and 4 ones
Multiple choice

4. What is the value of the 5 in 5,218?

  1. 5,000
  2. 500
  3. 50
  4. 5

Use exact math language

Use exact math language

Read the complete number and check the role of zero.

Multiple choice

5. What is the numeral for 'four hundred six'?

  1. 406
  2. 4,006
  3. 460
  4. 46
Multiple choice

6. Which number is greater: 570 or 507?

  1. 570
  2. 507
  3. They are equal.
  4. It cannot be determined.
Multiple choice

7. A learner writes 3,050 as '3 thousands, 5 hundreds'. Which correction is right?

  1. 3 thousands and 5 tens
  2. 3 hundreds and 5 tens
  3. 3 thousands and 5 ones
  4. 3 hundreds and 5 ones
Multiple choice

8. Which sentence correctly describes regrouping?

  1. 10 ones can be renamed as 1 ten.
  2. 10 tens equal 1 one.
  3. 1 hundred equals 10 ones.
  4. A regrouped number always gets larger.

Quick-check answers

  1. 1. 4,305
    4 thousands + 3 hundreds + 0 tens + 5 ones = 4,305.
  2. 2. 600 + 7
    607 contains 6 hundreds, 0 tens and 7 ones.
  3. 3. 2 thousands and 4 tens
    2,040 = 2,000 + 40; its hundreds and ones places are zero.
  4. 4. 5,000
    The 5 occupies the thousands place.
  5. 5. 406
    Four hundreds plus six ones gives 406; zero occupies the tens place.
  6. 6. 570
    Both have 5 hundreds, but 570 has 7 tens and 507 has 0 tens.
  7. 7. 3 thousands and 5 tens
    The 5 in 3,050 is in the tens place, worth 50, not 500.
  8. 8. 10 ones can be renamed as 1 ten.
    Equivalent regrouping changes the units but not the total value.

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