Complete the exercises related to decimals as specified in the image.

Understand the Problem

The question is asking students to work through various math exercises involving decimals, including matching numbers to their representations, identifying digit places in a number, building decimals based on specific criteria, expressing numbers as decimals or fractions, and continuing sequences of numbers.

Answer

1. a) \( 8 \), b) \( 4 \), c) \( 1 \), d) \( 6 \) 2. a) \( 4.7 \), b) \( 58.96 \), c) \( 5.78 \) 3. a) \( 1.3 \), b) \( 0.27 \), c) \( 14.2 \), d) \( 8.43 \), e) \( 0.05 \) 4. a) \( \frac{11}{100} \), b) \( \frac{4}{5} \), c) \( \frac{11}{10} \), d) \( \frac{307}{100} \), e) \( \frac{146}{25} \) 5. a) \( 2.1, 2.2, 2.3 \), b) \( 5.95, 5.96, 5.97 \), c) \( 12.1, 12.2, 12.3 \), d) \( 8.00, 8.01, 8.02 \), e) \( 6.05, 6.06, 6.07 \), f) \( 4.26, 4.27, 4.28 \)

Steps to Solve

Identify Digit Places in 186.45
For the number 186.45:
- Tens place: The digit is ( 8 ).
- Tenths place: The digit is ( 4 ).
- Hundreds place: The digit is ( 1 ).
- Ones place: The digit is ( 6 ).
Build Decimals With Given Digits
a. Build a decimal with ( 7 ) in the tenths place and ( 4 ) in the ones place:
The decimal is ( 4.7 ).

b. Build a decimal with ( 9 ) in the tenths place, ( 6 ) in the hundredths place, ( 8 ) in the ones place, and ( 5 ) in the tens place:
The decimal is ( 58.96 ).

c. Build a decimal with ( 5 ) in the ones place, ( 7 ) in the tenths place, and ( 8 ) in the hundredths place:
The decimal is ( 5.78 ).
Express as a Decimal
a. Convert ( \frac{13}{10} ) to decimal:
Result: ( 1.3 ).

b. Convert ( \frac{27}{100} ) to decimal:
Result: ( 0.27 ).

c. Convert ( \frac{142}{10} ) to decimal:
Result: ( 14.2 ).

d. Convert ( \frac{843}{100} ) to decimal:
Result: ( 8.43 ).

e. Convert ( \frac{5}{100} ) to decimal:
Result: ( 0.05 ).
Express as a Fraction
a. Convert ( 0.11 ) to fraction:
Result: ( \frac{11}{100} ).

b. Convert ( 0.8 ) to fraction:
Result: ( \frac{8}{10} ) or simplified to ( \frac{4}{5} ).

c. Convert ( 1.1 ) to fraction:
Result: ( \frac{11}{10} ).

d. Convert ( 3.07 ) to fraction:
Result: ( \frac{307}{100} ).

e. Convert ( 5.84 ) to fraction:
Result: ( \frac{584}{100} ) or simplified to ( \frac{146}{25} ).
Next Three Numbers in Each Sequence
a. For sequence ( 1.5, 1.6, 1.7, 1.8, 1.9, 2.0 ):
Next three numbers: ( 2.1, 2.2, 2.3 ).

b. For sequence ( 5.92, 5.93, 5.94 ):
Next three numbers: ( 5.95, 5.96, 5.97 ).

c. For sequence ( 11.8, 11.9, 12.0 ):
Next three numbers: ( 12.1, 12.2, 12.3 ).

d. For sequence ( 7.97, 7.98, 7.99 ):
Next three numbers: ( 8.00, 8.01, 8.02 ).

e. For sequence ( 6.02, 6.03, 6.04 ):
Next three numbers: ( 6.05, 6.06, 6.07 ).

f. For sequence ( 4.23, 4.24, 4.25 ):
Next three numbers: ( 4.26, 4.27, 4.28 ).

a. ( 8 )
b. ( 4 )
c. ( 1 )
d. ( 6 )
a. ( 4.7 )
b. ( 58.96 )
c. ( 5.78 )
a. ( 1.3 )
b. ( 0.27 )
c. ( 14.2 )
d. ( 8.43 )
e. ( 0.05 )
a. ( \frac{11}{100} )
b. ( \frac{4}{5} )
c. ( \frac{11}{10} )
d. ( \frac{307}{100} )
e. ( \frac{146}{25} )
a. ( 2.1, 2.2, 2.3 )
b. ( 5.95, 5.96, 5.97 )
c. ( 12.1, 12.2, 12.3 )
d. ( 8.00, 8.01, 8.02 )
e. ( 6.05, 6.06, 6.07 )
f. ( 4.26, 4.27, 4.28 )

More Information

This exercise reinforces understanding of decimals and fractions, showing how they can represent the same value in different forms. It's useful in everyday situations like finance or measurement.

Tips

Confusing tenths and hundredths when identifying places; remember that tenths are to the right of the decimal and are the first position.
Simplifying fractions incorrectly; always check for common factors.
Not continuing sequences correctly, especially with decimals; careful counting is essential.

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