Question

write the value of the underlined digit.

1. 2.51
2. 83.22
3. 41.07
4. 98.62
5. a baker has 100 oranges and uses 23 of them to make orange juice. what portion of the oranges are used? write your answer as a decimal.

______ of the oranges

1. you fill a beaker $2\frac{70}{100}$ times for an experiment. write this number as a decimal.
2. your friend writes $6\frac{50}{100}$ as 5.60. is your friend correct? explain.
3. shade each model to show 0.30 and 0.3. what do you notice?

two models: a grid and a bar graph

1. you work on a puzzle with 100 pieces. you connect 64 of the puzzle pieces. what portion of the puzzle have you completed? write your answer as a decimal.

______ of the puzzle
what portion of the puzzle do you have left to complete? write your answer as a decimal.
______ of the puzzle

Explanation:

Step1: Identify place value (Q13)

Underlined digit 2 is in ones place: $2 \times 1 = 2$

Step2: Identify place value (Q14)

Underlined digit 2 is in hundredths place: $2 \times \frac{1}{100} = 0.02$

Step3: Identify place value (Q15)

Underlined digit 4 is in tens place: $4 \times 10 = 40$

Step4: Identify place value (Q16)

Underlined digit 2 is in hundredths place: $2 \times \frac{1}{100} = 0.02$

Step5: Calculate orange portion (Q17)

Divide used by total: $\frac{23}{100} = 0.23$

Step6: Convert mixed number to decimal (Q18)

Convert fraction part: $2 + \frac{70}{100} = 2 + 0.70 = 2.70$

Step7: Check friend's conversion (Q19)

Convert mixed number: $6 + \frac{50}{100} = 6 + 0.50 = 6.50$

Step8: Analyze decimal equivalence (Q20)

0.30 = $\frac{30}{100}$, shade 30/100 grid; 0.3 = $\frac{3}{10}$, shade 3/10 grid. They represent the same value.

Step9: Calculate completed puzzle portion (Q21a)

Divide connected by total: $\frac{64}{100} = 0.64$

Step10: Calculate remaining puzzle portion (Q21b)

Subtract completed from 1: $1 - 0.64 = 0.36$

Answer:

1. 2
2. 0.02
3. 40
4. 0.02
5. 0.23
6. 2.70
7. No, the correct decimal is 6.50, not 5.60. The whole number part should be 6, not 5.
8. When shading, 30 small squares in the 100-square grid (for 0.30) and 3 out of 10 columns in the 10-column grid (for 0.3) are shaded. Notice that 0.30 and 0.3 are equivalent values.
9. Completed: 0.64; Remaining: 0.36