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Answer :
Let's evaluate each expression to see if they correctly represent the decimal 57.036. We'll address each option systematically:
(A) [tex]\(57 + \frac{3}{100} + \frac{6}{1,000}\)[/tex]
- Breaking this down:
- [tex]\(57\)[/tex] is the whole number part.
- [tex]\(\frac{3}{100} = 0.03\)[/tex], which represents the tenths and hundredths places for the decimal.
- [tex]\(\frac{6}{1,000} = 0.006\)[/tex], which represents the thousandths place.
- Adding these up: [tex]\(57 + 0.03 + 0.006 = 57.036\)[/tex].
- This expression is correct.
(B) [tex]\(57 + 3 \times \frac{10}{1,000} + 6 \times \frac{10}{1,000}\)[/tex]
- Breaking this down:
- [tex]\(57\)[/tex] is the whole number part.
- [tex]\(3 \times \frac{10}{1,000} = 3 \times 0.01 = 0.03\)[/tex]
- [tex]\(6 \times \frac{10}{1,000} = 6 \times 0.01 = 0.06\)[/tex]
- Adding these up: [tex]\(57 + 0.03 + 0.06 = 57.09\)[/tex].
- This expression does not represent 57.036.
(C) [tex]\(57 + 36 \times 0.01\)[/tex]
- Breaking this down:
- [tex]\(57\)[/tex] is the whole number part.
- [tex]\(36 \times 0.01 = 0.36\)[/tex]
- Adding these up: [tex]\(57 + 0.36 = 57.36\)[/tex].
- This expression does not represent 57.036.
(D) [tex]\(57 + 36 \times 0.001\)[/tex]
- Breaking this down:
- [tex]\(57\)[/tex] is the whole number part.
- [tex]\(36 \times 0.001 = 0.036\)[/tex]
- Adding these up: [tex]\(57 + 0.036 = 57.036\)[/tex].
- This expression is correct.
(E) "fifty-seven and thirty-six hundredths"
- The term "thirty-six hundredths" would be written as 0.36, not 0.036.
- Therefore, this does not match 57.036, but rather represents 57.36.
- This expression is incorrect for 57.036.
Based on this evaluation, the correct expressions that represent the decimal 57.036 are options (A) and (D).
(A) [tex]\(57 + \frac{3}{100} + \frac{6}{1,000}\)[/tex]
- Breaking this down:
- [tex]\(57\)[/tex] is the whole number part.
- [tex]\(\frac{3}{100} = 0.03\)[/tex], which represents the tenths and hundredths places for the decimal.
- [tex]\(\frac{6}{1,000} = 0.006\)[/tex], which represents the thousandths place.
- Adding these up: [tex]\(57 + 0.03 + 0.006 = 57.036\)[/tex].
- This expression is correct.
(B) [tex]\(57 + 3 \times \frac{10}{1,000} + 6 \times \frac{10}{1,000}\)[/tex]
- Breaking this down:
- [tex]\(57\)[/tex] is the whole number part.
- [tex]\(3 \times \frac{10}{1,000} = 3 \times 0.01 = 0.03\)[/tex]
- [tex]\(6 \times \frac{10}{1,000} = 6 \times 0.01 = 0.06\)[/tex]
- Adding these up: [tex]\(57 + 0.03 + 0.06 = 57.09\)[/tex].
- This expression does not represent 57.036.
(C) [tex]\(57 + 36 \times 0.01\)[/tex]
- Breaking this down:
- [tex]\(57\)[/tex] is the whole number part.
- [tex]\(36 \times 0.01 = 0.36\)[/tex]
- Adding these up: [tex]\(57 + 0.36 = 57.36\)[/tex].
- This expression does not represent 57.036.
(D) [tex]\(57 + 36 \times 0.001\)[/tex]
- Breaking this down:
- [tex]\(57\)[/tex] is the whole number part.
- [tex]\(36 \times 0.001 = 0.036\)[/tex]
- Adding these up: [tex]\(57 + 0.036 = 57.036\)[/tex].
- This expression is correct.
(E) "fifty-seven and thirty-six hundredths"
- The term "thirty-six hundredths" would be written as 0.36, not 0.036.
- Therefore, this does not match 57.036, but rather represents 57.36.
- This expression is incorrect for 57.036.
Based on this evaluation, the correct expressions that represent the decimal 57.036 are options (A) and (D).
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