Question

Which number equals 7 thousandths? (A) \(0.7\) (B) \(0.07\) (C) \(0.007\) (D) 7,000

Short answer

The number that equals 7 thousandths is (C) \(0.007\).

Step-by-step solution

Understand Decimal Place Values

The decimal place values are as follows: - Tens: \(10^1 = 10\) - Ones: \(10^0 = 1\) - Tenths: \(10^{-1} = 0.1\) - Hundredths: \(10^{-2} = 0.01\) - Thousandths: \(10^{-3} = 0.001\) We are looking for the decimal representation of 7 thousandths.

Identify the Decimal Representation of 7 Thousandths

Since we are looking for 7 thousandths, we need to represent the number such that the digit 7 is placed in the thousandths position. Looking at the options provided: (A) \(0.7\) → This number represents 7 tenths, not thousandths. (B) \(0.07\) → This number represents 7 hundredths, not thousandths. (C) \(0.007\) → This number represents the correct place value, with 7 in the thousandths position. (D) 7,000 → This number represents 7 thousand, not thousandths.

Choose the Correct Answer

The number that equals 7 thousandths is the one with the digit 7 placed in the thousandths position. From the given options, the correct answer is: (C) \(0.007\)

Key concepts

Understanding Decimals

Decimals are numbers that consist of a whole number part and a fractional part, separated by a decimal point. This system is crucial for representing values that are not whole, like 0.5 or 2.75. When reading decimals, the digits to the right of the decimal point represent parts of one whole. Understanding how to read these decimal fractions is fundamental. For example, the number 0.7 is read as 'seven tenths,' while 0.03 is 'three hundredths.' Decimals can express values in a finer granularity than whole numbers, allowing for more precise calculations. This is why understanding decimals is so essential in everyday math problems as well as in advanced mathematical concepts.

Place Value Positions

Place value positions refer to the location of digits in a number and determine the value that each digit represents. In a decimal, each place to the left of the decimal point is ten times greater than the one to its right, and each place to the right of the decimal point is ten times smaller.

• The first digit after the decimal is the tenths place, resembling fractions like 1/10 or 0.1.
• The second digit is the hundredths place, representing values like 1/100 or 0.01.
• The third digit is the thousandths place, equating to 1/1000 or 0.001.

Correctly identifying place value positions is critical for accurate math problem-solving with decimals. For example, in the number 0.007, the digit 7 is in the thousandths place, indicating seven parts out of a thousand.

Math Problem-Solving

Solving math problems involving decimals entails recognizing the place value of each digit and understanding the decimal that represents the given fraction. In the original exercise, you were asked to find which number equals 7 thousandths. To solve such problems, follow these steps:

• First, understand what the term thousandths means, representing it as a fraction 1/1000 or decimal 0.001.
• Next, identify the position for the specified decimal part in the number. Here, it requires placing the number 7 in the thousandths position. Thus, it reads as 0.007.
• Finally, compare the options given and select the number that fits the place value requirement.

Effective math problem-solving depends on a clear grasp of decimal places and the role of each digit. Thus, practice recognizing and applying decimal values to become proficient in mathematical tasks.