Question

example
1 in the example, what does the 0 in 1.046 mean?
2 fill in the missing information in the table below.
words
three and seventy-two hundredths
mixed number
expanded form
decimal

Explanation:

1. For the question about the 0 in 1.046

Step1: Analyze the place - value of each digit in 1.046

In the decimal number \(1.046\), the digit \(1\) is in the units place (\(1\times1\)), the digit \(0\) is in the tenths place (\(0\times\frac{1}{10}\)), the digit \(4\) is in the hundredths place (\(4\times\frac{1}{100}\)), and the digit \(6\) is in the thousandths place (\(6\times\frac{1}{1000}\)).

2. For filling in the table for "three and seventy - two hundredths"

Step1: Mixed - number form

The fraction part of the mixed number for "seventy - two hundredths" is \(\frac{72}{100}\). So the mixed number is \(3\frac{72}{100}\)

Step2: Expanded - form (fractional)

\(3+\frac{72}{100}=3 + \frac{70 + 2}{100}=3+\frac{70}{100}+\frac{2}{100}=3+\frac{7}{10}+\frac{2}{100}\). In the form of \(a\times1 + b\times\frac{1}{10}+c\times\frac{1}{100}\), we have \(3\times1+0\times\frac{1}{10}+7\times\frac{1}{10}+2\times\frac{1}{100}\) (the \(0\times\frac{1}{10}\) is because there is no digit in the tenths place for non - decimal expansion in terms of base - 10 fractions in this step of breaking down \(\frac{72}{100}\) further).

Step3: Decimal form

\(3\frac{72}{100}=3 + 0.72=3.72\)

Answer:

1. The \(0\) in \(1.046\) means \(0\) tenths (or \(0\times\frac{1}{10}\)).

2.

• Mixed Number: \(3\frac{72}{100}\)
• Expanded Form: \(3\times1+0\times\frac{1}{10}+7\times\frac{1}{10}+2\times\frac{1}{100}\)
• Decimal: \(3.72\)