Question

The blue whale (Balaenoptera musculus) is thought to be the largest animal ever to inhabit Earth. The longest blue whale ever observed had a length of $33\mathrm{m}$. What is this length in millimeters?

Short answer

The length in millimeters is 33,000 mm.

Step-by-step solution

Understand the Unit Conversion

We need to convert the length from meters to millimeters. Knowing the conversion factor is crucial: There are 1000 millimeters in a meter.

Set Up the Conversion Calculation

Since 1 meter equals 1000 millimeters, the length in millimeters can be found by multiplying the length in meters by 1000.

Perform the Calculation

Given the length of the blue whale is 33 meters, multiply 33 by 1000 to convert to millimeters. The calculation is:$$33\text{ meters}\times 1000\frac{\text{millimeters}}{\text{meter}}=33000\text{ millimeters}$$

Interpret the Result

The length of the longest blue whale observed, when expressed in millimeters, is 33,000 millimeters. This final step ensures we comprehend the conversion and aren't misled by errors in calculation steps.

Key concepts

Metric System

The metric system is a decimal system of measurement that is used worldwide, particularly in science and engineering. It's designed to be simple and intuitive, with units that are based on powers of ten. This makes conversions within the system straightforward since they usually involve just shifting the decimal point.
For example, the basic unit of length in the metric system is the meter. Other units of length derive from the meter by multiplying or dividing by powers of ten. This means that:

• Kilometers (km) are 1,000 times larger than a meter
• Centimeters (cm) are 1/100th of a meter
• Millimeters (mm) are 1/1,000th of a meter

This uniformity allows for easy conversion between units simply by multiplying or dividing by factors of ten, making it the preferred system for scientific measurements and simplifying calculations like converting meters to millimeters.

Length Measurement

Length measurement is a fundamental part of physics and everyday life. Measuring length allows us to determine how much space an object or distance covers. In the metric system, the meter is the standard unit of length, providing a common ground for measuring various objects, from tiny insects to colossal whales.
When dealing with different scales, we use metric multiples and submultiples of the meter. For instance, a blue whale's length is often measured in meters due to its enormous size. However, for smaller objects, like nail length, millimeters or centimeters might be more convenient. Length is measured along a single dimension, unlike area or volume, which account for two and three dimensions, respectively.
Understanding these basic principles of length measurement in the metric system ensures clarity and convenience, especially when resizing or converting measurements for practical applications.

Conversion Factor

A conversion factor is a numeric multiplier that allows you to change one unit of measurement into another. It's key to understand these factors when performing unit conversions, as they ensure accuracy in calculations.
In the context of converting meters to millimeters, the conversion factor is 1,000. This means there are 1,000 millimeters in one meter, making the conversion straightforward. For example, to convert a length measurement like a blue whale's 33 meters into millimeters, you'd multiply by this factor: $$33\times 1000=33,000\text{ millimeters}$$
This process involves three clear steps: identify the current unit and the unit to convert to, determine the appropriate conversion factor, and then perform the multiplication or division. When you correctly apply conversion factors, you ensure your measurements are accurate and understandable, regardless of the initial unit.