Problem 47 - Algebra 1: Concepts and Skills

Question

Complete the statement using \(<,>,\) or \(=\). \(\frac{3}{1000} ? 0.03\)

Step-by-Step Solution

Answer

\(\frac{3}{1000} < 0.03\)

Step 1: Convert the Fraction to a Decimal

To start off, convert the fraction \(\frac{3}{1000}\) into a decimal. This can be achieved by dividing the numerator (3) by the denominator (1000).

Step 2: Compare the Decimal Values

After converting \(\frac{3}{1000}\) into decimal form, compare this decimal to 0.03.

Key Concepts

Fractions

Fractions are a way of representing numbers that are not whole. They consist of a numerator, the top number, and a denominator, the bottom number. The numerator tells you how many parts you have, while the denominator tells you how many parts make up a whole. For example, in the fraction \( \frac{3}{1000} \), 3 is the numerator and 1000 is the denominator. This fraction signifies that we have 3 parts out of a total of 1000.

Understanding fractions can sometimes be challenging because they can look similar to each other but represent different values. A good way to think about fractions is by visualizing them as pieces of a pie. If a pie is divided into 1000 equal slices, then having 3 slices would be equivalent to \( \frac{3}{1000} \).

• Numerator: Number of parts you have.
• Denominator: Number of equal parts the whole is divided into.

Remember, to convert a fraction into a decimal, you need to divide the numerator by the denominator. This forms a crucial step when comparing fractions to decimals.

Decimals

Decimals are another way of representing numbers with a fractional component, using powers of 10. They are often used because they integrate well with the decimal (base 10) numeral system that we use daily. For instance, the number 0.03 uses the decimal point to show that it's three hundredths of a whole number.

To write fractions as decimals, you divide the numerator by the denominator. In our example, \( \frac{3}{1000} \) when divided results in 0.003. This decimal indicates that it is three-thousandths of a whole. Learning to convert fractions to decimals can simplify many math problems, allowing for easier computation and comparison.

• Decimal Point: Indicates the fractional part of a number.
• Decimals are based on powers of ten.

With decimals, you can precisely represent and compare values that fractions might make more cumbersome.

Comparing Numbers

Comparing numbers is an essential math skill that involves determining the relative size of numbers, whether they are fractions, decimals, or whole numbers. The symbols \( < \), \( > \), and \( = \) are used to express these relationships:

• \( < \): Less Than
• \( > \): Greater Than
• \( = \): Equal To

To compare fractions and decimals effectively, it's best to convert all numbers to the same form—typically decimals. Once both numbers are decimals, you can easily see which is larger by comparing their digits, starting from the left.

In our specific exercise, we convert \( \frac{3}{1000} \) to 0.003 and compare it to 0.03. By lining up the decimals, it's clear that 0.003 is less than 0.03, so \( \frac{3}{1000} < 0.03 \). Practicing comparisons helps improve number sense and ensures accuracy in mathematical computations.