Decimal Place Value

• How decimal notation extends the Indian place-value system to tenths, hundredths, and thousandths after the decimal point.
• To read and write decimals in money (₹ and paise) and measurement (metres, centimetres, kilograms).
• To express decimals in expanded form and compare digit values by place.
• To link decimals with fractions — especially tenths and hundredths from NCERT Math-Magic 5, Chapter 10 (Tenths and Hundredths).

Level 1 — Place value after the decimal point

Verbal: Each digit after the decimal point has a place value ten times smaller than the digit to its left.

Symbolic: In 6.408 → 6 ones, 4 tenths (0.4), 0 hundredths, 8 thousandths (0.008).

NCERT link (Math-Magic 5, Ch 10): Price tags like ₹45.75 and lengths like 1.7 m appear throughout Tenths and Hundredths.

Level 2 — Money, expanded form, and trailing zeros

Verbal: 100 paise = ₹1, so 50 paise = ₹0.50 = fifty hundredths of a rupee.

Symbolic: ₹12.50 = 12 + 0.5 = 12 + 50/100; 2.34 = 2 + 0.3 + 0.04.

Real-life: A notebook costs ₹35.00; a pen ₹12.50; total ₹47.50 — read each place before paying.

Read ₹127.05 and write it in expanded decimal form.

Step 1 — Whole part: 127 rupees.
Step 2 — Decimal part: 0.05 = 0 tenths + 5 hundredths = 5 paise.
Step 3 — Expanded: 100 + 20 + 7 + 0 + 0.05.
Answer: One hundred twenty-seven rupees and five paise.

In 6.408, which digit is in the hundredths place?

Step 1 — After decimal: 4 = tenths, 0 = hundredths, 8 = thousandths.
Answer: The digit 0 is in the hundredths place (value 0.00).

• Write nine hundredths as a decimal. (0.09)
• Express 3 + 0.2 + 0.05 as one decimal. (3.25)
• In 8.306, what is the value of the digit 3? (3 tenths = 0.3)
• Which is greater: 0.6 or 0.59? Explain using place value.
• Stretch: ₹100 − ₹45.75 = ? Write the answer in rupees and paise. (₹54.25)

Revision tip: Draw a place-value chart with columns Ones · Tenths · Hundredths · Thousandths. Write three price tags from your home (₹) and label each digit's value.

Open the Practice tab for graded questions on Decimal Place Value.

• Use the platform-native live simulation or PhET-style tool for this topic (number line, Venn, physics playground, molecule builder, sensor dashboard, etc.).
• Mirror / body / home activity: physically do the concept (count objects, measure, role-play) and photograph or describe for portfolio.
• Voice or text reflection with AI Mentor: explain the concept to a younger student or family member.

• "Explain this concept to a Class 6 student using one real example from an Indian home, school, market, or festival."
• "What is one common mistake students make here, and how would you catch yourself making it?"
• Stretch: "How does this connect to coding, robotics, money, health, environment, or a future career?"

• Complete the core practice + one extension activity (photo, table, short reflection, or mini-project) for base XP + topic badge.
• 5-7 day streak or family discussion note = multiplier + visible artifact in parent/principal dashboard.
• Best real-world application stories (anonymised) featured on class or national leaderboard.

• One hands-on project or measurement using the Drishti kit or household items that makes the concept physical.
• Direct link to at least one Future Skill track (Money Management, Green Tech, Cyber Defenders, Micro-Entrepreneurship, AI Mastery, Sustainable Living, Personality Development).
• Coding extension where relevant (simple script, simulation, or data logging).

This material emphasises experiential "learning by doing", competency (apply/create/analyse), vocational exposure, critical thinking, and multidisciplinary connections. Designed to feed live worlds, AI Mentor (with memory), gamification, robotics, parent analytics, and future skills — not just exam prep.

Portfolio Evidence Idea: Your photo/table/reflection/project + one sentence on "How this helps me in real life or a possible future path."

Open the Practice tab for aligned questions (easy/medium/hard + case-based) with full AI scaffolding.

See curriculum for cross-links and the full future-skills/robotics chapters.