Decimal Operations
Arithmetic with decimals and understanding place value
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Have you ever tried to buy a $4.99 video game skin with exactly five one-dollar bills? The cashier gives you back one tiny penny. That penny is a decimal in action! 🎮 Decimals are just fractions wearing cool disguises, helping us measure things that are in-between whole numbers. Whether you're timing a 100-meter dash or figuring out exactly how much pizza is left, decimals are your best friends. 🍕
On the SSAT, Decimal Operations are all about knowing where to put that tiny, super-important dot. Think of place value like a VIP seating chart at a concert. The seats to the left of the decimal point are for the big whole numbers (ones, tens, hundreds). The seats to the right are for the smaller pieces (tenths, hundredths, thousandths). The further right you go, the tinier the piece gets!
When adding or subtracting decimals, there is one golden rule: Line up the dots! If you keep the decimal points straight up and down, the math is just like regular addition. When multiplying, you can pretend the decimal points are invisible at first. Just multiply the numbers, and at the end, count how many digits were behind the decimals in the problem to put the dot back in its rightful place. 🕵️♂️ Master the dot, and you'll crush the SSAT decimal questions!
Practice Questions
3 practice questions for SSAT Upper Level
What is the value of the underlined digit in the number above?
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- In a decimal number, the first digit to the right of the decimal point is in the tenths place, the second digit is in the hundredths place, and the third digit is in the thousandths place. In the number , the digit is in the tenths place, the digit is in the hundredths place, and the digit is in the thousandths place. Therefore, the underlined digit represents 7 hundredths.
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- First, calculate the total cost of the notebooks: . The notebooks cost $12.75. Next, calculate the total cost of the pens: . The pens cost $3.60. Add these to find the total spent: . Maria spent $16.35. Finally, subtract from $20.00 to find the change: . Maria receives $3.65 in change.
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- To find the total distance traveled, multiply the speed by the time: . First, multiply the numbers as if there were no decimal points: . Next, count the total number of decimal places in the original factors. There is one decimal place in and one decimal place in , making a total of two decimal places. Move the decimal point in the product two places to the left: , which simplifies to miles.
Tips & Strategies
- When adding or subtracting decimals of different lengths, fill in the empty spaces with zeros! For example, change into . It makes the math so much easier to see. 👀
- If a question asks you to compare decimals, line them up on top of each other by the decimal point and fill in zeros. It's much easier to see that is bigger than !
Common Mistakes
- Watch out for lining up the numbers instead of the decimal points when adding! is NOT . If you line up the dots, it's .
- Don't forget that a shorter decimal can actually be bigger than a longer one! is bigger than because 4 tenths is more than 1 tenth.
Frequently Asked Questions
Do I need to line up the decimal points when multiplying?
Nope! Only for adding and subtracting. When multiplying, just stack the numbers normally, multiply, and then count up the total decimal places at the very end.
How do I remember the place value names to the right of the dot?
They all end in 'ths'! It goes tenths, hundredths, thousandths. Think of it like a lisp: 'I have one tenTH of a pizza left!'
Are decimals and fractions the same thing?
Yes! They are just two different ways of writing the exact same thing. is just wearing a disguise.
Can I use a calculator on the SSAT?
No calculators are allowed on the SSAT! 🚫 That's why practicing these decimal tricks on paper is super important.