Problem 14 - Prealgebra

Question

Write each number as a fraction or a mixed number. Do not reduce your answers. $$12.045$$

Step-by-Step Solution

Answer

12.045 as a mixed number is \(12\frac{45}{1000}\).

Step 1: Understand the Decimal

The number given is 12.045. This decimal can be split into a whole number and a fractional part: 12 is the whole number, and 0.045 is the fractional part.

Step 2: Convert the Fractional Part to a Fraction

The fractional part 0.045 can be written as \(\frac{45}{1000}\). This is because 45 is in the thousandths place in the decimal.

Step 3: Combine the Whole and Fractional Parts

Combine the whole number part and the fractional part into a mixed number. Therefore, 12.045 is written as \(12\frac{45}{1000}\).

Key Concepts

Decimal to Fraction Conversion

Converting decimals to fractions is a key skill in mathematics. It's all about expressing the same number in two different ways. When a decimal is transformed into a fraction, you show how many parts of a whole you have, using a numerator and a denominator.

To convert a decimal to a fraction, follow these steps:

• Identify the decimal part of the number. For instance, in 12.045, the decimal part is 0.045.
• Count how many decimal places are there. Here, you have three decimal places, which corresponds to the thousandths place.
• Use the decimal places to determine the denominator. Since 0.045 has three decimal places, the denominator will be 1000.
• Write the decimal as a fraction, with the denominator as a power of 10. Therefore, 0.045 becomes \(\frac{45}{1000}\).

This process lets you take a decimal, like 12.045, and express it as a combination of a whole number and a fraction: \(12\frac{45}{1000}\).

Understanding Mixed Numbers

Mixed numbers combine whole numbers and fractions, offering a way to express quantities that aren't whole but also aren't completely fractional. When you see a number like 12.045, it can be expressed as a mixed number because it includes both a whole part (12) and a portion of a smaller unit (0.045 as the fraction \(\frac{45}{1000}\)).

To write a mixed number from a decimal:

• First, separate the whole number and the decimal part. In 12.045, the whole part is 12.
• Convert the decimal to a fraction, as explained above. Here, 0.045 is \(\frac{45}{1000}\).
• Combine these into one expression: \(12\frac{45}{1000}\).

This mixed number tells us we have 12 whole units and 45 out of 1000 of another unit. It's a tidy way to represent decimal quantities as a combination of whole and partial amounts.

Place Value in Decimals

Place value is a fundamental way of understanding how numbers are structured. In the decimal system, each place to the right of the decimal point represents a fraction of ten, with a different power of ten making up each place.

For example, in the number 12.045:

• The '0' is in the tenths place, meaning 0 tenths.
• The '4' is in the hundredths place, representing 4 hundredths or \(\frac{4}{100}\).
• The '5' is in the thousandths place, representing 5 thousandths or \(\frac{5}{1000}\).

Understanding the place value helps in converting decimals to fractions because it directly informs you what the denominator of the fraction should be. With 0.045, recognizing the thousandths place tells you the fraction is \(\frac{45}{1000}\). This process is the essence of decimal to fraction conversion, embedding the decimal's place value into the fraction's structure.