112r. Review Decimals, Place Value and Conversions

Learning Intentions

• To understand place value in a decimal
• compare two or more decimals to decide which is largest
• convert decimals to fractions
• convert some simple fractions to decimals

Pre-requisite Summary

• Know that whole numbers Use place value columns such as ones, tens and hundreds
• Understand that the decimal point separates whole-number parts from fractional parts
• Know that tenths, hundredths and thousandths are parts of a whole
• Be able to compare whole numbers by place value
• Understand that fractions represent parts of a whole
• Recall simple equivalent fractions such as and
• Know that a fraction can be written in different forms with the same value
• Be able to Simplify fractions

Worked Examples

Worked Example 1

State the value of the underlined digit:

a) In , the digit

b) In , the digit

c) In , the digit

Worked Example 2

Write each decimal in expanded form:

a)

b)

c)

Worked Example 3

Compare the decimals and state which is largest:

a) and

b)

c) and

Worked Example 4

Convert each decimal to a fraction:

a)

b)

c)

Worked Example 5

Convert each simple fraction to a decimal:

a)

b)

c)

Worked Example 6

Convert each simple fraction to a decimal:

a)

b)

c)

Problems

Problem 1

State the value of the underlined digit:

a) In , the digit

b) In , the digit

c) In , the digit

Problem 2

Write each decimal in expanded form:

a)

b)

c)

Problem 3

Compare the decimals and state which is largest:

a) and

b)

c) and

Problem 4

Convert each decimal to a fraction:

a)

b)

c)

Problem 5

Convert each simple fraction to a decimal:

a)

b)

c)

Problem 6

Convert each simple fraction to a decimal:

a)

b)

c)

Exercises

Understanding and Fluency

Exercise 1.

State the place value of the underlined digit:

a) In , the digit

b) In , the digit

c) In , the digit

d) In , the digit

Exercise 2.

Write each decimal in expanded form:

a)

b)

c)

d)

Exercise 3.

Compare each pair of decimals Use or :

a)

b)

c)

d)

Exercise 4.

Put these decimals in order from smallest to largest:

a)

b)

c)

Exercise 5.

Convert each decimal to a fraction:

a)

b)

c)

d)

Exercise 6.

Convert each decimal to a fraction in simplest form where possible:

a)

b)

c)

d)

Exercise 7.

Convert each simple fraction to a decimal:

a)

b)

c)

d)

Exercise 8.

Convert each simple fraction to a decimal:

a)

b)

c)

d)

Reasoning

Exercise 9.

Explain why is greater than even though is greater than .

Exercise 10.

A student says that is larger than because is larger than . Explain the mistake.

Exercise 11.

Noah says that and are different numbers because one has more digits. Is he correct? Explain.

Exercise 12.

Explain why .

Exercise 13.

A student says that because the denominator is . Describe the error.

Problem-solving

Exercise 14.

A bottle contains L of water and another contains L. Which bottle contains more water?

Exercise 15.

A runner completed races in s, s and s. Which time was the greatest?

Exercise 16.

A ribbon is m long. Write this length as a fraction of a metre in simplest form.

Exercise 17.

A container is filled to of its capacity. Write this as a decimal.

Exercise 18.

A student scored on one task and on another. Which score is greater?

Exercise 19.

A number has ones, tenths, hundredths and thousandths. Write the decimal and then write it as a fraction.

Potential Misunderstandings

• Students may think digits after the decimal point work like whole numbers rather than place values
• Students may confuse tenths and hundredths
• Students may think a longer decimal is always greater
• Students may compare decimals by ignoring the place value of each digit
• Students may not Recognise that trailing zeros do not change the value of a decimal, for example
• Students may write a decimal as a fraction but forget to use the correct denominator such as , or
• Students may not simplify decimal fractions when required
• Students may think converting a fraction to a decimal changes the value
• Students may confuse with instead of
• Students may not see that some simple fractions can be converted by using known equivalent fractions with denominator or

Next: 113r. Review Operations with Decimals