Pre-Algebra

What is the number in standard decimal form? (9x100)+(4x10)+(8x1)+(2x1/10)+(5x1/100)

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Solve each multiplication in parentheses

We calculate each term on its own first. The first three give whole numbers. The last two give decimal values because we are multiplying by fractions less than 1.
2

Identify each digit's place value

Each term represents one place value in our number. This is called expanded form — it shows exactly what each digit is worth.
3

Add all terms together

Now we simply add all the values. Line them up by decimal point to make sure each digit lands in the right place.
4

Write the final standard decimal

Adding from left to right: 900 + 40 = 940, then + 8 = 948, then + 0.2 = 948.2, then + 0.05 = 948.25. This is the number in standard decimal form.

Understanding this problem

Learning Insight

Expanded form breaks a number into the value of each digit based on its position. Every digit's position is worth 10 times more than the position to its right, which is the foundation of our base-10 number system. The digits after the decimal point work the same way — just with fractions (tenths, hundredths, etc.) instead of whole numbers.

Quick Tip

When you see 1/10, just move the decimal one place to the left, and 1/100 moves it two places left. So 2 × 1/10 = 0.2 and 5 × 1/100 = 0.05 — quick and easy!

Common Mistake

Students often write 0.2 + 0.05 as 0.7 by adding the digits 2 and 5 without aligning the decimal places. Always line up decimals before adding — 0.20 + 0.05 = 0.25, not 0.7.