Question

Using abbreviations and the rules of the metric system, express the following quantities correctly. Three hundredths of a milliliter ______

Short answer

0.03 mL or 3 x 10^-2 mL

Step-by-step solution

Understand the given quantity

The problem states "three hundredths of a milliliter." This means we have to consider the value as a fraction of one milliliter. Three hundredths refers to the fraction \( \frac{3}{100} \).

Convert to decimal or power of ten

Three hundredths can be expressed in decimal form as \( 0.03 \). Alternatively, it can be represented in scientific notation as \( 3 \times 10^{-2} \).

Identify the correct metric abbreviation

The quantity given is in milliliters, which is abbreviated as 'mL.' The metric system uses 'm' as the abbreviation for 'milli,' which represents a factor of \( 10^{-3} \).

Express the quantity correctly

To express the given quantity in metric system notation using the abbreviation for milliliters: - When using decimal notation: \( 0.03 \text{ mL} \)- When using scientific notation: \( 3 \times 10^{-2} \text{ mL} \)

Key concepts

Abbreviations

Abbreviations are handy shortcuts in science and math, helping to simplify the way we communicate measurements. In the metric system, each measurement unit is represented by a specific abbreviation. These abbreviations allow us to quickly identify and work with units without writing out the full word. For example, the unit 'meter' is abbreviated as 'm', 'liter' as 'L', and in this exercise, the focus is on 'milliliter,' which is abbreviated as 'mL.'
The metric system itself is built on a series of prefixes that denote specific powers of ten. The prefix 'milli,' represented by 'm,' indicates that the unit is one-thousandth of the base unit. So, 'milliliter' means one-thousandth of a liter. This system of prefixes and abbreviations makes it easy to handle large and small measurements.
Using the correct abbreviation ensures clarity and prevents misunderstandings in communication. So, when we represent quantities accurately, especially in scientific contexts, it becomes essential to know and use these notation systems correctly.

Scientific Notation

Scientific notation is a way to express very large or very small numbers efficiently. It helps simplify calculations by using powers of ten. In this method, a number is written as the product of a number (between 1 and 10) and a power of ten.
For the exercise problem, three hundredths of a milliliter is expressed in scientific notation as \(3 \times 10^{-2}\). Here's how it works:

• The number 3 is placed in front, representing the significant figures we want to keep.
• The exponent \(-2\) indicates the decimal point is moved two places to the left from the number 3.

Scientific notation is especially useful in scientific and engineering fields, making complex calculations more manageable and reducing the risk of error when dealing with many zeroes. It provides a consistent method to express numbers regardless of their size.

Decimal Representation

Decimal representation is the expression of numbers using the base-ten system, which is the most commonly used numeral system. In the exercise, the term "three hundredths" is converted into a decimal as \(0.03\). This is achieved by dividing three by one hundred, thus, \(\frac{3}{100} = 0.03\).
Decimal notation is straightforward and intuitive for most people. It involves placing numbers to the right of a decimal point to reflect fractions of a whole. Each position represents a power of ten.

• For instance, in \(0.03\), the digit 3 is in the hundredths place.

Decimals are used worldwide in arithmetic operations, providing an easy way to add, subtract, multiply, and divide without the need for fractions. By understanding decimal representation, you can easily convert between fractions and decimals, enhancing your mathematical fluency and precision in everyday calculations.