'Five and eighty-three thousandths' means 5 + 83/1000. Since we need 83 in the thousandths place, we write 0.083 for the decimal part, giving us 5.083. Choice B represents eighty-three hundredths. Choice C represents eight hundred thirty thousandths. Choice D represents fifty-eight and three tenths.

When you read decimal numbers aloud, you need to understand place value positions after the decimal point. In 9.672, the digits after the decimal represent tenths, hundredths, and thousandths respectively.

Let's break down 9.672: The 9 is in the ones place, so we say "nine." After "and" (which represents the decimal point), we have 672 in the decimal places. The 6 is in the tenths place, the 7 is in the hundredths place, and the 2 is in the thousandths place. When reading decimals, you read all the digits after the decimal point as a whole number, then name the place value of the last digit.

So 672 is read as "six hundred seventy-two," and since the last digit (2) is in the thousandths place, we say "six hundred seventy-two thousandths." The blank in the statement asks for the first digit of this decimal portion, which is 6.

Answer choice (C) six is correct because 6 is the first digit in "six hundred seventy-two thousandths."

Answer choice (A) two is the last digit in the decimal portion, not the first. Answer choice (B) seven is the middle digit (in the hundredths place). Answer choice (D) sixty-seven combines the first two digits but doesn't match how we read the complete decimal portion.

Remember: when reading decimals, identify each place value position, then read all decimal digits as one number followed by the place value of the rightmost digit.

When you see a decimal written in expanded form like this, you need to convert it back to standard form first, then figure out how to read it aloud. This tests your understanding of place values and how to express decimals in words.

Let's work through the expanded form: $$4 \times 1 + 7 \times 0.1 + 2 \times 0.01 + 9 \times 0.001$$. This gives us $$4 + 0.7 + 0.02 + 0.009 = 4.729$$.

To read 4.729 aloud, remember that the whole number part (4) is read as "four," then you say "and" for the decimal point, then read the decimal part (729) as if it's a whole number but end with the place value of the last digit. Since 9 is in the thousandths place, you read it as "seven hundred twenty-nine thousandths."

Choice A reads the decimal part as if 4 isn't there - "forty-seven and twenty-nine thousandths" would be 47.029, not 4.729. Choice B incorrectly identifies the place value as hundredths instead of thousandths, which would be 4.729 rounded or a different number entirely. Choice C treats the entire number as if it's all in the decimal part, reading it as a fraction over 1000, which completely ignores the whole number 4.

The correct answer is D: "Four and seven hundred twenty-nine thousandths."

Study tip: Always convert expanded form to standard form first, then remember the pattern: [whole number] and [decimal digits as words] [place value of last digit].

When you encounter decimal numbers that need to be written in word form, you must carefully identify the place value of each digit after the decimal point. The number 7.450 kg has three digits after the decimal point, which means you're working in the thousandths place.

Let's break down 7.450: The whole number part is 7, and the decimal part is .450. To read the decimal portion correctly, look at the rightmost digit's place value. Since there are three decimal places, the last digit (0) is in the thousandths place. This means you read .450 as "four hundred fifty thousandths" - not hundredths or ten-thousandths.

The complete answer is "seven and four hundred fifty thousandths kilograms," which is choice D.

Now let's see why the other answers are wrong:

Choice A says "four hundred fifty-thousandths" with a hyphen, which would mean 450/1000000 (four hundred fifty millionths) - completely different from what we want.

Choice B treats .450 as if it only has two decimal places, calling it "forty-five hundredths." This ignores the zero in the thousandths place and changes the value entirely.

Choice C says "four hundred five thousandths," which would be written as .405, not .450. This mixes up the digit positions.

Remember this key strategy: always count the total number of decimal places to determine the place value name, and read all the digits as one complete number in that place value. The rightmost digit determines whether you're dealing with tenths, hundredths, thousandths, etc.

When you see a decimal that needs to be written in expanded form using fractions, think about place value. Each digit after the decimal point has a specific place: tenths, hundredths, thousandths, and so on.

Let's break down 0.875 step by step. The 8 is in the tenths place, so it represents $$\frac{8}{10}$$. The 7 is in the hundredths place, so it represents $$\frac{7}{100}$$. The 5 is in the thousandths place, so it represents $$\frac{5}{1000}$$. Therefore, 0.875 = $$\frac{8}{10} + \frac{7}{100} + \frac{5}{1000}$$, which is answer choice C.

Let's examine why the other options are incorrect. Choice A shows $$\frac{8}{10} + \frac{75}{1000}$$, which treats the last two digits (75) as a single unit in the thousandths place. This doesn't follow proper place value rules. Choice B has $$\frac{8}{100} + \frac{7}{10} + \frac{5}{1000}$$, which switches the place values of 8 and 7. This would actually equal 0.785, not 0.875. Choice D shows $$\frac{87}{100} + \frac{5}{10}$$, which groups the first two digits together and puts 5 in the wrong place value, giving us 0.87 + 0.5 = 1.37.

Remember this key strategy: when converting decimals to expanded fractional form, work from left to right after the decimal point. Each digit gets its own fraction with the denominator matching its place value (10 for tenths, 100 for hundredths, 1000 for thousandths).

Looking at the expanded form, the non-zero digits are: 5 (ones place), 8 (hundredths place), and 4 (thousandths place). The largest non-zero digit is 8, which is in the hundredths place. Choice A incorrectly focuses on the digit's overall size rather than comparing non-zero digits. Choice C incorrectly identifies position rather than digit size. Choice D identifies a place value with a zero digit.

Decimals can be written in different forms, such as numerals and simplified expansions. Reading 0.904 by place value involves 'nine hundred four thousandths,' with tenths (9 as 0.9), hundredths (0), and thousandths (4 as 0.004). Expanded form can be 0.9 + 0.004, omitting the zero hundredths. Digits link to values through their positions: the 4 is 4 × 0.001 = 0.004. A misconception is equating 0.904 to 0.94 by ignoring places, but 0.904 is actually less than 0.940. Multiple representations clarify such differences. They support better problem-solving in areas like precision and equivalence.

Decimals can be written in different forms, such as numerals, words, and expanded form. Reading decimals by place value involves grouping the decimal part, like naming 9.015 as 'nine and fifteen thousandths' to reflect the places. Writing in expanded form is summing like 9 + 0.01 + 0.005 for 9.015. Each digit connects to its value: in 9.015, the 0 is 0 tenths, 1 is 1 hundredth, and 5 is 5 thousandths. A common misconception is expanding to hundredths incorrectly, like 'nine and fifteen hundredths' for 9.15. Multiple representations are useful for interpreting readings like temperatures. They ensure accurate communication and understanding across applications.

Decimals can be written in different forms, like words and expanded notation, to represent the same value. Reading by place value for 5.018 means saying 'five and eighteen thousandths,' where tenths is zero, hundredths is one (0.01), and thousandths is eight (0.008). Expanded form breaks it into 5 + 0.01 + 0.008, omitting the zero tenths. Digits connect to values via their places: the 8 in thousandths is 8 × 0.001 = 0.008, not in tenths as 0.8. A misconception is misplacing digits, such as thinking the 8 is in tenths, which would incorrectly make it 5.818. Multiple representations enhance comprehension and error-checking. They are essential for accurate communication in math and science.

Decimals can be written in different forms, such as numerals, words, and expanded form. Reading decimals by place value requires specifying each digit's position, like in 1.230 where 1 is ones, 2 is tenths, 3 is hundredths, and 0 is thousandths. Writing in expanded form is summing like 1 + 0.2 + 0.03 + 0 for 1.230. Each digit connects to its value: the 2 is 2 x 0.1, not in hundredths as some might think. A common misconception is that a trailing zero increases the value, but 1.230 equals 1.23. Multiple representations are useful for describing measurements like a pet's mass. They foster clarity and prevent misunderstandings in scientific contexts.