Question

Measurement Convert each measurement to meters. Write your answers as both fractions and decimals. \(700 \mathrm{mm}\)

Short answer

Fraction: \( \frac{7}{10} \), Decimal: 0.7 meters.

Step-by-step solution

Understand the Conversion Factor

To convert millimeters to meters, note that 1 meter equals 1,000 millimeters. Therefore, the conversion factor is \(1 \text{ meter} = 1,000 \text{ millimeters}\).

Set Up the Conversion Calculation

To convert 700 millimeters to meters, use the conversion factor. This can be written as \(700 \text{ mm} \times \frac{1 \text{ meter}}{1,000 \text{ mm}}\).

Perform the Calculation

Multiply 700 by \( \frac{1}{1,000} \). The result in meters is \( \frac{700}{1,000} \).

Simplify the Fraction

Simplify the fraction \( \frac{700}{1,000} \) by dividing the numerator and the denominator by their greatest common divisor, which is 100. This gives \( \frac{7}{10} \).

Convert the Fraction to Decimal

Convert the simplified fraction \( \frac{7}{10} \) to a decimal. This gives 0.7.

Write the Final Answer

The final answer in both fraction and decimal form is: Fraction: \( \frac{7}{10} \), Decimal: 0.7 meters.

Key concepts

Converting Units of Measurement

Measurement conversion is a fundamental skill in mathematics that involves changing a quantity from one unit to another. Here, you are converting millimeters to meters. One key factor to remember is the conversion factor. For instance, 1 meter is equal to 1,000 millimeters. This means if you have millimeters and want to convert them to meters, you divide by 1,000. Understanding the conversion factor is crucial to avoid mistakes. To convert 700 millimeters to meters, you use this formula: \( 700 \text{ mm} \times \frac{1 \text{ meter}}{1,000 \text{ mm}} \). Always keep track of your units and ensure that they cancel out appropriately, leaving you with the desired unit. The calculation can then be simplified for clarity.

Fractions and Decimals

When working with measurement conversions, it is often necessary to express your answers in both fractions and decimals. This allows for greater clarity and precision. In this exercise, after performing the calculation, you get \( \frac{700}{1,000} \) meters. Simplifying this fraction involves dividing the numerator and the denominator by their greatest common divisor (GCD), which is 100 in this case. So, \( \frac{700}{1,000} = \frac{7}{10} \).
To convert this fraction to a decimal, you divide the numerator by the denominator: \( 7 \div 10 = 0.7 \). Thus, \( \frac{7}{10} \) is equivalent to 0.7 meters. Practicing these conversions between fractions and decimals strengthens your mathematical fluency and flexibility, making you better equipped to handle different types of problems.

Mathematics Education

Learning to convert units and work with fractions and decimals is a key part of mathematics education. These skills are essential not just in academic settings but also in real-life situations, such as measuring ingredients for a recipe or determining distances on a map. Building a strong foundation in these basic concepts helps students develop problem-solving abilities and logical thinking. Engaging with exercises like converting 700 millimeters to meters helps solidify your understanding of measurement units. Regular practice of these types of problems is recommended to gain confidence and proficiency. Use visual aids like number lines or measurement charts to help understand these conversions more intuitively. Remember, the goal is to make these concepts second nature, reducing the cognitive load when encountering similar problems in more complex mathematics or daily life scenarios.