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📝 Composing and Decomposing Decimals
This page contains solutions for exercises in Mathematics for Grade 5, First Term, following the Egyptian curriculum. The topic covered is Composing and Decomposing Decimals.
Question 1: Complete the following.
a. 5 Tenths = ___ Hundredths.
To convert tenths to hundredths, we multiply by 10 because there are 10 hundredths in every tenth.
Calculation: \( 5 \times 10 = 50 \)
b. 5.17 read as five and seventeen ___.
When reading a decimal, we read the whole number part, say "and" for the decimal point, and then read the decimal part as a whole number, followed by the place value of the last digit.
In 5.17, the last digit (7) is in the hundredths place.
c. Fifty-eight and thirty-six thousandths in standard form is ___.
"Fifty-eight" is the whole number part: 58.
"Thirty-six thousandths" means the last digit (6) must be in the thousandths place (the third decimal place). So, we write it as 0.036.
Combining them: \( 58 + 0.036 = 58.036 \)
d. The value of the digit 0 in the number 45.209 is ___.
The digit 0 is in the hundredths place. The value of a digit is the digit itself multiplied by its place value.
However, the value of the digit 0 is always 0, regardless of its position in the number.
e. The place value of the digit 3 in the decimal number 2.3 is ___.
The place value describes the position of a digit. The digit 3 is the first digit to the right of the decimal point.
This position is called the tenths place.
Question 2: Write each of the following in word form.
a. 4.014
1. Read the whole number part: "Four".
2. Say "and" for the decimal point.
3. Read the number after the decimal: "fourteen".
4. State the place value of the last digit (4), which is in the thousandths place.
b. 0.207
1. There is no whole number part, so we start with the decimal part.
2. Read the number after the decimal: "two hundred seven".
3. State the place value of the last digit (7), which is in the thousandths place.
c. 40.14
1. Read the whole number part: "Forty".
2. Say "and" for the decimal point.
3. Read the number after the decimal: "fourteen".
4. State the place value of the last digit (4), which is in the hundredths place.
d. 500.005
1. Read the whole number part: "Five hundred".
2. Say "and" for the decimal point.
3. Read the number after the decimal: "five".
4. State the place value of the last digit (5), which is in the thousandths place.
Question 3: Choose the correct answer.
a. Sixty-one and five thousandths is ___.
"Sixty-one" is the whole number part: 61.
"Five thousandths" means the digit 5 is in the third decimal place: 0.005.
Combining them gives 61.005.
b. 2.4 > ___
We need to find a number that is less than 2.4. Let's compare the choices:
- A. 2.40 is equal to 2.4.
- B. 4.2 is greater than 2.4.
- C. 1.956 is less than 2.4.
- D. 3.5 is greater than 2.4.
c. Which of the following is true?
Let's evaluate each statement:
- A. 0.832 > 0.837 is false because 2 is less than 7 in the thousandths place.
- B. \( \frac{16}{10} = 1.6 \) is true.
- C. 0.1 + 3 < 1.3 is false because 3.1 is not less than 1.3.
- D. 1.019 > 1.1 is false because 0 is less than 1 in the tenths place.
d. \( 4.7 \times 1,000 = \) ___
When multiplying by 1,000, we move the decimal point three places to the right.
4.7 -> 47.0 -> 470.0 -> 4700.0
e. The value of the digit 7 in the number 2.347 is ___.
The digit 7 is in the third position after the decimal point, which is the thousandths place.
So, its value is 7 thousandths, or 0.007.
f. \( 250 + 0.2 + 0.05 = \) ___
We compose the number by adding the parts together:
250 (whole number) + 0.2 (tenths) + 0.05 (hundredths) = 250.25
g. In the problem \( 74.8 \div 10 \), the value of the digit 4 decreased from 4 to ___.
First, solve the division: \( 74.8 \div 10 = 7.48 \).
In the original number (74.8), the digit 4 is in the ones place, so its value is 4.
In the new number (7.48), the digit 4 is in the tenths place, so its value is 0.4 or \( \frac{4}{10} \).