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Question 29

Make a place value table similar to the one above. Write each quantity in decimal form and in terms of place value, and read the number:

(a) 2 ones, 3 tenths and 5 hundredths

(b) 1 ten and 5 tenths

(d) 1 hundred, 1 one and 1 hundredth

(e) $\dfrac{8}{100}$ and $\dfrac{9}{10}$

(f) $\dfrac{5}{100}$

(g) $\dfrac{1}{10}$

(h) $2\dfrac{1}{100}$ , $4\dfrac{1}{10}$ and $7\dfrac{7}{1000}$

Solution

Understand the Question

Each place value represents a specific power or fractional power of $10$ $10$ :
- Hundreds: $100$
- Tens: $10$
- Ones: $1$
- Tenths: $\dfrac{1}{10} = 0.1$
- Hundredths: $\dfrac{1}{100} = 0.01$
- Thousandths: $\dfrac{1}{1000} = 0.001$
To write any number in decimal form, multiply each digit by its place value, add them together, and write in standard decimal notation.
Numbers after the decimal point are read digit by digit (for example, $2.35$ is read as "Two point three five").

\begin{array}{|c|c|c|c|c|c|c|c|} \hline \text{Part} & \text{Hundreds } (100) & \text{Tens } (10) & \text{Ones } (1) & \text{Tenths } \left(\dfrac{1}{10}\right) & \text{Hundredths } \left(\dfrac{1}{100}\right) & \text{Thousandths } \left(\dfrac{1}{1000}\right) & \text{Decimal Form} \\ \hline \text{(a)} & 0 & 0 & 2 & 3 & 5 & 0 & 2.35 \\ \hline \text{(b)} & 0 & 1 & 0 & 5 & 0 & 0 & 10.5 \\ \hline \text{(c)} & 0 & 0 & 4 & 0 & 6 & 0 & 4.06 \\ \hline \text{(d)} & 1 & 0 & 1 & 0 & 1 & 0 & 101.01 \\ \hline \text{(e)} & 0 & 0 & 0 & 9 & 8 & 0 & 0.98 \\ \hline \text{(f)} & 0 & 0 & 0 & 0 & 5 & 0 & 0.05 \\ \hline \text{(g)} & 0 & 0 & 0 & 1 & 0 & 0 & 0.1 \\ \hline \text{(h)} & 0 & 1 & 3 & 1 & 1 & 7 & 13.117 \\ \hline \end{array}

(a) 2 ones, 3 tenths and 5 hundredths

Step 1 · Find Place Value Expansion and Decimal Value

Diagram 1

Place value expansion $2 \times 1 + 3 \times \dfrac{1}{10} + 5 \times \dfrac{1}{100} = 2 + 0.3 + 0.05 = 2.35$

Read as: "Two point three five"

Answer

(a) Decimal: $2.35$
Place value: $2 \times 1 + 3 \times \dfrac{1}{10} + 5 \times \dfrac{1}{100}$
Read as: Two point three five

(b) 1 ten and 5 tenths

Step 1 · Find Place Value Expansion and Decimal Value

Diagram 2

Place value expansion $1 \times 10 + 0 \times 1 + 5 \times \dfrac{1}{10} = 10 + 0 + 0.5 = 10.5$

Read as: "Ten point five"

Answer

(b) Decimal: $10.5$
Place value: $1 \times 10 + 0 \times 1 + 5 \times \dfrac{1}{10}$
Read as: Ten point five

(c) 4 ones and 6 hundredths

Step 1 · Find Place Value Expansion and Decimal Value

Diagram 3

Place value expansion $4 \times 1 + 0 \times \dfrac{1}{10} + 6 \times \dfrac{1}{100} = 4 + 0 + 0.06 = 4.06$

Read as: "Four point zero six"

Answer

(c) Decimal: $4.06$
Place value: $4 \times 1 + 0 \times \dfrac{1}{10} + 6 \times \dfrac{1}{100}$
Read as: Four point zero six

(d) 1 hundred, 1 one and 1 hundredth

Step 1 · Find Place Value Expansion and Decimal Value

Diagram 4

Place value expansion $1 \times 100 + 0 \times 10 + 1 \times 1 + 0 \times \dfrac{1}{10} + 1 \times \dfrac{1}{100} = 100 + 0 + 1 + 0 + 0.01 = 101.01$

Read as: "One hundred one point zero one"

Answer

(d) Decimal: $101.01$
Place value: $1 \times 100 + 0 \times 10 + 1 \times 1 + 0 \times \dfrac{1}{10} + 1 \times \dfrac{1}{100}$
Read as: One hundred one point zero one

(e) $\dfrac{8}{100}$ and $\dfrac{9}{10}$

Step 1 · Find Place Value Expansion and Decimal Value

Diagram 5

Place value expansion $0 \times 1 + 9 \times \dfrac{1}{10} + 8 \times \dfrac{1}{100} = 0 + 0.9 + 0.08 = 0.98$

Read as: "Zero point nine eight"

Answer

(e) Decimal: $0.98$
Place value: $0 \times 1 + 9 \times \dfrac{1}{10} + 8 \times \dfrac{1}{100}$
Read as: Zero point nine eight

(f) $\dfrac{5}{100}$

Step 1 · Find Place Value Expansion and Decimal Value

Diagram 6

Place value expansion $0 \times 1 + 0 \times \dfrac{1}{10} + 5 \times \dfrac{1}{100} = 0 + 0 + 0.05 = 0.05$

Read as: "Zero point zero five"

Answer

(f) Decimal: $0.05$
Place value: $0 \times 1 + 0 \times \dfrac{1}{10} + 5 \times \dfrac{1}{100}$
Read as: Zero point zero five

(g) $\dfrac{1}{10}$

Step 1 · Find Place Value Expansion and Decimal Value

Diagram 7

Place value expansion $0 \times 1 + 1 \times \dfrac{1}{10} = 0 + 0.1 = 0.1$

Read as: "Zero point one"

Answer

(g) Decimal: $0.1$
Place value: $0 \times 1 + 1 \times \dfrac{1}{10}$
Read as: Zero point one

(h) $2\dfrac{1}{100}$ , $4\dfrac{1}{10}$ and $7\dfrac{7}{1000}$

Step 1 · Convert Mixed Fractions and Sum

Diagram 8

Convert each mixed fraction into decimal form $2\dfrac{1}{100} = 2 + 0.01 = 2.01$ $4\dfrac{1}{10} = 4 + 0.1 = 4.1$ $7\dfrac{7}{1000} = 7 + 0.007 = 7.007$

Add the decimal numbers

\begin{aligned} 2.01 + 4.1 + 7.007 &= (2 + 4 + 7) + (0.01 + 0.1 + 0.007) \\[0.6em] &= 13 + 0.117 \\[0.6em] &= 13.117 \end{aligned}

Place value expansion $1 \times 10 + 3 \times 1 + 1 \times \dfrac{1}{10} + 1 \times \dfrac{1}{100} + 7 \times \dfrac{1}{1000}$

Read as: "Thirteen point one one seven"

Answer

(h) Decimal: $13.117$
Place value: $1 \times 10 + 3 \times 1 + 1 \times \dfrac{1}{10} + 1 \times \dfrac{1}{100} + 7 \times \dfrac{1}{1000}$
Read as: Thirteen point one one seven

Common Mistakes

Missing Zero Placeholders: Writing 6 hundredths as $0.6$ instead of $0.06$ . Tenths is the first position after the decimal, and hundredths is the second.
Incorrect Reading of Decimals: Reading digits after the decimal point as whole numbers (e.g., reading $2.35$ as "Two point thirty-five" instead of "Two point three five").
Mixed Fraction Sums: Forgetting that $2\dfrac{1}{100} = 2.01$ and $4\dfrac{1}{10} = 4.10$ ; always align decimal points vertically when adding decimals.

Question 29

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