Problem 93 - Prealgebra

Question

Write the decimal number in words. i) A recently discovered 7.03-carat blue diamond auctioned at Sotheby’s. ii) The newly launched European Planck telescope will stay in orbit 1.75 years measuring radiation from the Big Bang. iii) The sun composes 0.9985 of the mass in our solar system. iv) Clay particles are small - only 0.0001 inch.

Step-by-Step Solution

Answer

Seven point zero three, one point seventy five, zero point nine nine eight five, zero point zero zero zero one.

Step 1: Understanding Decimal Notation

Decimals are numbers that have a whole number part and a fractional part separated by a decimal point. For example, in 7.03, the 7 is the whole number part, and the 03 is the fractional part.

Step 2: Converting Whole Numbers to Words

Write the whole number part in words. For 7.03, 7 is written as 'seven'. Similarly, for 1.75 and 0.9985, 1 is 'one' and 0 is zero (though it's often omitted).

Step 3: Converting Decimal Fractions to Words

For the decimal part, start with 'point' after the whole number, then write each digit individually. In 7.03, 'point zero three'. In 0.0001, 'point zero zero zero one', and in 0.9985, 'point nine nine eight five'.

Step 4: Complete Number Phrase

Once the whole number and decimal have been converted, combinethem into the complete phrase. For 7.03, say 'seven point zero three'. For 1.75, it's 'one point seventy five'. For 0.9985, it's 'zero point nine nine eight five'. For 0.0001, it's 'zero point zero zero zero one'.

Key Concepts

Decimal Notation

Decimal notation helps us express numbers with precision by using a point to separate the integer (whole number) part from the fractional part. This is crucial in various scientific and mathematical contexts. Think of the decimal point as a bridge linking the whole number with its fractions. For instance, in the number 7.03, the decimal point is between the whole number 7 and the fractional part 03.

Decimal notation becomes particularly useful when dealing with measurements or calculations that require a high degree of accuracy. Whether you're noting the weight of a diamond or measuring distances in space, decimals allow a detailed description that's not possible with whole numbers alone.

You can think of decimals as an extended form of fractions, where each place to the right of the decimal represents a power of 10. This means that every step increments from tenths, to hundredths, to thousandths, and so on.

Whole Number

Whole numbers in a decimal are the numbers found to the left of the decimal point. This part of a number represents the complete units and does not account for any fractional quantity. In 7.03, the 7 is the whole number.

Whole numbers are straightforward to convert into words. Here’s how you do it in practice:

• Identify the numbers to the left of the decimal point.
• Convert this number into words. For 7.03, you have 'seven'.

The whole number remains consistent no matter the fractional part. So, whether it's 7.03 or 7.99, the initial whole number 'seven' stays the same.

Remember, a whole number is the anchor of the number, providing a base value before delving into the fractional complexities that follow the decimal.

Fractional Part

The fractional part of a decimal is everything that appears after the decimal point, detailing the division of the whole into smaller parts. In a number like 1.75, the fractional part is 75. This section represents tenths, hundredths, or even smaller divisions of a unit.

When writing the fractional part in words, start after saying 'point'; each digit is spelled out individually:

• In 0.9985, say 'point nine nine eight five'.
• For 0.0001, it becomes 'point zero zero zero one'.

These individual words help ensure clarity, especially with small or elongated fractions. By clearly stating each digit, you avoid confusion, especially in precise applications like scientific measurements.

Understanding the fractional part in words keeps you accurate and prevents the misinterpretation of important numerical information.

Converting Numbers to Words

Turning numbers into words is an important skill, allowing us to communicate effectively in spoken and written forms. Follow these steps to change any decimal number into its word format:

• Identify the whole number part: Say the complete number that lies to the left of the decimal point in words. For instance, for 7.03, say 'seven'.
• Use the word 'point': This signals that you are moving to the digits following the decimal.
• State each digit individually: For 7.03, say 'seven point zero three'. Each number after the decimal needs its own word.

This method not only ensures that the numerical information stays intact but also communicates it in a universally comprehensible way. It maintains accuracy and prevents misinterpretation, crucial in fields such as science, finance, and education.

Remember, each component of the number should be distinct when using this conversion technique, enabling precise and clear communication.